Assignment: Week 3 Exercise

Course: Math 201(B2) Summmer 2014

1)      Determine which of the following nubers could not represent the probability of an event.

0,0.025,-0.7,60%,660/1299.55/42

Choose the correct answer

2. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space

Randomly choosing a multiple of 3 between 1 and 20

3. Determine the number of outcomes in the event. Decide weather the event is a simple event or not.

    You randomly select one card from a standard deck. Event C is selecting a red ace.

4. You randomly select one card from a standard deck. Event A is selecting a three. Determine the number of outcomes in event A. Then decide whether the event is a simple event or not.

 The number of outcomes in the event A is —

Is event A a simple event?

5. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

    If you roll a six sided die six times, you will roll an even number at least one.

    Choose the correct answer below.

6. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 123?

Choose the correct probability below.

7. Consider a company that selects employees for random drug tests. The company uses a computer to randomly select employees’ numbers that range from 1 to 5632. Find the probability of selecting a number less than 1000. Find the probability of selecting a number greater than 1000.

8. A family has four children. Use the tree diagram to answer each question.

9. You go to work for three days. Make an on-time/late tree diagram for the three days.

    Choose the correct tree diagram below.

10. What is the probability that a registered voter voted in the election?

11. Use the frequency distribution, which shows the responses of a survey of college students when asked “How often do you wear a seat belt when riding in a car driven by someone else?” Find the following probabilities of responses of college students from the survey chosen at random.

12. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employees chosen at random is B. 

13.  When two purple flowers (RB) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring’s, red (RR), purple(RB) and blue(bb). If two purple snapdragons are crossed. What is the probability that the offspring will be (a) purple,(b) red and (c) blue?

14. Determine whether the events E and F are independent or dependent. Justify your answer.

a)      E: A person having a high GPA

F: The same person being highly organized.

b)      E: A randomly selected person coloring her hair black.

F: Another randomly selected person coloring her hair blond.

c)       E: The war in a major oil-exporting country.

F: The price of gasoline.

15. Researcher found that people with depression are three times more likely to have a breathing related sleep disorder than people who are not depressed. Identify the two events described in the study. Do the results indicated that the events are independent or dependents?

Identify the two events. Choose the correct answer below.

Are the event independent or depedent?

16. In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Eight out of 10 women  with this mutation develop breast cancer.

a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.

c. Are the events of carrying this mutation and developing breast cancer independent or dependent?

17. The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year.

Table.

a)      Find the probability that a randomly selected family is not taking summer vacation this year.

b)      Find the probability that a randomly selected family owns a computer

c)       Find the probability a randomly selected family is taking a summer vacation this year given that they own a computer.

      d. Find the probability a randomly selected family is taking a summer vacation this year  and owns a computer.

e). Are the events of owing a computer and taking a summer5 vacation this year independent or dependent events?

18. Suppose 90% of kids who visits a doctor have a fever and 25% of kids with a fever have sore throats. What’s the probability that a kids who goes to the doctor has a fever and a sore throats.?

19. The table below shows the result of a survey in which 141 men and 145 women workers ages 25 to 64 were asked if they have at least one month ‘s income set aside for emergencies.

Complete parts (a) through (d)

Tabel:

(a)    Find the probability that a randomly selected worker has one month’s income or more set aside for emergencies.

(b)   Given that a randomly selected worker is a male, find the probability that the worker has less than one month’s income.

(c)    Given that a randomly selected worker has one month’s income or more, , find the probability that the worker is a female.

(d)   Are the events “having less than one month’s income saved “ and being male” independent or dependent?

20.          About 19% of the population of a large country is hopelessly romantic. If two are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?

21. A distribution center receives shipments of a products from three different factories in the quantities of 60, 40 and 20. Three times a product is selected at random, each time without replacement. Find the probability that (a) all three products come from the third factory and (b) none of the here products come from the third factory.

22. By rewriting the formula for the multiplication rule, you can rewrite a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B/ A) = P(A and B)/P(A). Use the information below to find the probability that  a  fight departed on time given that it arrives on time.

The probability that an airplane flight departs on time is 0.89.

The probability that a flight arrive on time is 0.87.

The probability that a flight departs and arrives on time is 0.82.

23. Determine whether the statement is true or false. If it is false, rewrite it as a true statement.

It two events are mutually exclusive; they have no outcomes in common.

Choose the correct answer below.

24. Decide if the events shown in the venn  diagram are mutually exclusive.

      Are the events mutually exclusive?

25. Decide if the events are mutually exclusive.

  Event A: Randomly selecting someone who owns a car.

  Event B: Randomly selecting a married male

Are the two events mutually exclusive?

26. During a 52- week period ,a company paid overtime wages for 19 weeks and hired temporary help for 9 weeks. During 5 weeks, the company paid overtime and hired temporary help.

Complete parts(a) and (b) below.

(a)    Are the event” selecting a week that contained overtime wages” and selecting a week that contained temporary help wages” mutually exclusive?

(b)   If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages.

27.          The percent distribution of live multiple- delivery births (three or more babies) in a particular year for women 15 to 54 years old shown in the pie chart. Find each probabilty.

Pie Chart ( number of multiple Birth)

a.       Randomly selecting a mother 30-39 years old.

b.      Randomly selecting a mother not 30 -39 years old.

c.       Randomly selcting a mother less than 45 years old.

d.      Randomly selecting a mother at least 20 year old.

28. Find P(A or B or C) for the given probabilities.

      P(A)=0.33, P(B)=0.23, P(C)=0.16

      P(A and B) = 0.13, P(A and C) =0.03, P(B and C) = 0.07

     P(A and B and C) = 0.01

29. Decide if the situation invovles permutations, combinations, or neither. Explain your resonsing.

      The number of ways a three – member committee can be chosen from 10 people.

      Does the situation involve permutaion , combinations or neither ? choose the correct answer below.

30. Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish and two different desserts. The astronauts can choose from 11 main dishes, 7 vegetable dishes and 12 desserts.  How many different meals are possible? 

31. Outside a home, there is an 8 –key keypad with letters A,B, C, D,E, F G & H that can be used to open the garage if the correct eight- letter code  is entered. Each key may be used only once. How many codes are possible.

32. Suppose Grant is going to burn a compact disk (CD) that will contain 11 songs. In how many ways can grant arrange the 11 songs on the CD?

MAT540

Week 8 Homework

Chapter 4

14.   Grafton Metalworks Company produces metal alloys from six different ores it mines.  The company has an order from a customer to produce an alloy that contains four metals according to the following specifications:  at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D.  The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:

When the metals are processed and refined, the impurities are removed. 

The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.

a.        Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer. 

19.   As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects.  It is up to the congressman to decide how to distribute the money.  The congressman has decided to allocate the money to four ongoing programs because of their importance to his district – a job training program, a parks project, a sanitation project, and a mobile library.  However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election.  His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows.

In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines:

·         None of the programs can receive more than 40% of the total allocation.

·         The amount allocated to parks cannot exceed the total allocated to both the sanitation  project and the mobile library

·         The amount allocated to job training must at least equal the amount spent on the sanitation project. 

Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all.  The congressman wants to know the amount to allocate to each program to maximize his votes. 

a.       Formulate a linear programming model for this problem.

b.      Solve the model by using the computer.

20.   Anna Broderick is the dietician for the State University football team, and she is attempting to determine a nutritious lunch menu for the team.  She has set the following nutritional guidelines for each lunch serving:

·         Between 1,500 and 2,000 calories

·         At least 5 mg of iron

·         At least 20 but no more than 60 g of fat

·         At least 30 g of protein

·         At least 40 g of carbohydrates

·         No more than 30 mg of cholesterol

She selects the menu from seven basic food items, as follows, with the nutritional contributions per pound and the cost as given: 

The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.

a.       Formulate a linear programming model for this problem.

b.      Solve the model by using the computer

c.       If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution?

22.   The Cabin Creek Coal (CCC) Company operates three mines in Kentucky and West Virginia, and it supplies coal to four utility power plants along the East Coast.  The cost of shipping coal from each mine to each plant, the capacity at each of the three mines and the demand at each plant are shown in the following table:

The cost of mining and processing coal is $62 per ton at mine 1,  $67 per ton at mine 2, and  $75 per ton at mine 3.  The percentage of ash and sulfur content per ton of coal at each mine is as follows:

Each plant has different cleaning equipment.  Plant 1 requires that the coal it receives have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined.    CCC wabts to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost. 

a.       Formulate a linear programming model for this problem.

b.      Solve this model by using the computer.

36.   Joe Henderson runs a small metal parts shop. The shop contains three machines – a drill press, a lathe, and a grinder.   Joe has three operators, each certified to work on all three machines.  However, each operator performs better on some machines than on others.  The shop has contracted to do a big job that requires all three machines.  The times required by the various operators to perform the required operations on each machine are summarized as follows: 

Joe Henderson wants to assign one operator to each machine so that the topal operating time for all three operators is minimized.

a.       Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer

c.       Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator.  Kelly can perform each of the three required machine operations in 20 minutes.  Should Joe hire his sister-in-law? 

43.   The Cash and Carry Building Supply Company has received the following order for boards in three lengths:

The company has 25-foot standard-length boards in stock.  Therefore, the standard-length boards must be cut into the lengths necessary to meet order requirements.  Naturally, the company wishes to minimize the number of standard-length boards used. 

a.       Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer

c.       When a board is cut in a specific pattern, the amount of board left over is referred to as “trim-loss.” Reformulate the linear programming model for this problem, assuming that the objective is to minimize trim loss rather than to minimize the total number of boards used, and solve the model.  How does this affect the solution? 

1.       Complete all 7 steps. Place work and answers, below each respective step. Expand the space as needed.

2.       Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.

3.       Word-process formulas using Equation Editor and diagrams using Drawing Tool.

Problem 1

Given y = f(x) = x² + 2x +3

a)      Use the definitional formula given below to find the derivative of the function.

b)      Find the value of the derivative at x = 3.

Problem 2

Given, y = f(x) = 2 x³ – 3x² + 4x +5

a)      Use the Power function to find derivative of the function.

b)      Find the value of the derivative at x = 4.

Problem 3

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.

R(x) = 16x – x²

C(x) = 20 + 4x

a)      Determine the profit function P(x).

b)      Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.

c)       Compute the break-even quantities.

d)      Determine the average cost at the break-even quantities.

e)      Determine the marginal revenue R’(x).

f)       Determine the marginal cost C’(x)

g)      At what quantity is the profit maximized?

As with most literary works, there are recurrent universal patterns in Harry Potter and the Sorcerer’s Stone. Consider the definition of Mythological Criticism:

A central concept in mythological criticism is the archetype, a symbol, character, situation, or image that evokes a deep universal response. The idea of the archetype came into literary criticism from the Swiss psychologist Carl Jung. Jung believed that all individuals share a “collective unconscious,” a set of primal memories common to the human race, existing below each person’s conscious mind. Critic Joseph Campbell identified archetypal symbols and situations in literary works by demonstrated how similar mythic characters appear in virtually every culture on every continent.

For your 1000 word written analysis, you will track the progress of Harry Potter as a Hero Archetype. Please follow our Hero’s Quest Outline and fill in ALL 12 story steps (as listed below). There are no “right” answers to this assignment – follow your instincts and describe what you deem important and necessary!

You will need to write specific examples of Harry’s hero quest, so keep a pen and pad handy as you read the novel. Please refer to specific scenes, characters, events, changes of consciousness and/or circumstance. Please include at least five (5) quotes with page numbers!

As you venture through the novel, think about what makes Harry a hero: How does his special world compare to his ordinary world? What actions can be deemed heroic? Who are Harry’s teachers and guides? What is his quest? Does his quest change during the course of the novel? Who are his allies or enemies? What challenges or conflicts does Harry need to overcome? How does Harry fit the hero archetype?

Your grade will be based on the thoroughness of your analysis (if you successfully respond to all 12 story steps!), the strength of your quotes/examples, and your thoughtfulness and openmindedness! You may write more than the 1000 word minimum, but please keep your analysis under 1,500 words! Please write in paragraph form – do not post an outline!

To receive maximum credit, please post your analysis via our Turnitin link on our Moodle course page page PRIOR to the whole-class forum discussion. Good luck and enjoy!

************************************************************************************************

12 Story Steps To The Myth — Please Respond to All 12!!!

Act One

(1) Ordinary World – Something is missing in this world. It’s the hero or hera’s present, everyday situation. It’s described in order to create a contrast. A question is raised.

(2) Call To Adventure – information is put into the hero or hera’s system, often brought by a messenger.

(3) Reluctant Hero or Hera

(4) Wise Old Person (most optional of steps) – Maybe gives message to trust the path.

Act Two

(5) Special World – Hero gets very committed by his will – or not.

(6) Tests, Allies & Enemies – Enmities and alliances are formed. What are the conditions to the quest? How will the hero react?

(7) Innermost Cave – Holds what the hero wants.

(8) Supreme Ordeal (at ¾ point in 2nd Act) – Hero surviving/transcending “death.”

(9) Seizing The Sword – Taking possession. Enjoying the spoils. But maybe something else chases the hero. Often a missing piece is introduced.

Act Three

(10) The Road Back

(11) Resurrection – Another hero’s test. Final proof – better if visual.

(12) Return with Elixir – To share with everyone.

STAT200 : Introduction to Statistics Final Examination, Page 1 of 6

STAT 200

OL4 / OL2 Sections

Final Exam

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.

Answer all 30 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted.

Record your answers and work on the separate answer sheet provided.

This exam has 300 total points.

You must include the Honor Pledge on the title page of your submitted final exam. Exams submitted without the Honor Pledge will not be accepted.

1. True or False. Justify for full credit. (25 pts)

(a) If there is no linear correlation between two variables, then these two variables are not related in any way.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 2 of 6

(b) If the variance from a data set is zero, then all the observations in this data set are identical.

(c) .ofcomplementtheis where,1)( AAAandAP 

(d) In a hypothesis testing, if the P-value is less than the significance level α, we reject the null hypothesis.

(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) Frequency

1.0 – 1.9 2

2.0 – 2.9 12

3.0 – 3.9 2

4.0 – 4.9 4

2. What percentage of the checkout times was less than 3 minutes? (5 pts)

3. In what class interval must the median lie? Explain your answer. (5 pts)

4. Calculate the mean of this frequency distribution. (5 pts)

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two decimal places) (10 pts)

Refer to the following data to answer questions 6, 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

2 15 15 18 40

6. Find the sample standard deviation. (Round the answer to two decimal places) (10 pts)

7. Find the coefficient of variation. (5 pts)

8. Are any of these study times considered unusual based on the Range Rule of Thumb?

Show work and explain. (5 pts)

Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.

Consider selecting one card at a time from a 52-card deck. Let event A be the first card is an ace, and event B be the second card is an ace. (Note: There are 4 aces in a deck of cards)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 3 of 6

9. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (10 pts) 10. If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (10 pts)

11. Are A and B independent when the selection is with replacement? Why or why not? (5 pts)

Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

12. What is the probability that a randomly selected junior is taking at least one of these two courses? (10 pts)

13. What is the probability that a randomly selected junior is taking PSYC300, given that

he/she is taking STAT200? (10 pts)

14. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10 qualified candidates. How many different ways can the officers be appointed? (5 pts)

15. Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven

books with her in a road trip. How many different ways can the three books be selected? (5 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below. Show all work. Just the answer, without supporting work, will receive no credit.

x -1 0 1 2

()Px 0.1 0.3 0.4 0.2

16. Determine the expected value of x. (5 pts)

17. Determine the standard deviation of x. (Round the answer to two decimal places) (10 pts)

Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 8 times.

18. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and

probability of failures (q), respectively? (5 pts)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 4 of 6

19. Find the probability that that she returns at least 1 of the 8 serves from her opponent. (10 pts)

20. How many serves can she expect to return? (5 pts)

Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

21. What is the probability that a randomly selected dogwood tree is greater than 12 feet? (5 pts)

22. Find the 75th percentile of the dogwood tree height distribution. (10 pts)

23. If a random sample of 36 dogwood trees is selected, what is the probability that the mean height

of this sample is less than 10 feet? (10 pts)

24. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will

receive no credit. (15 pts)

25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the 0.05



 level.

750:

750:

1

0









H

H

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the critical values. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(c) What is your conclusion of the test? Please explain. (20 pts)

26. Consider the hypothesis test given by

5.0:

5.0:

1

0





pH

pH

In a random sample of 225 subjects, the sample proportion is found to be 51.0ˆ p .

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 5 of 6

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of 0

H at the 0.01



 level?

Explain. (20 pts)

27. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 15 3 11 9

4 13 12

5 12 12

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours?

Assume we want to use a 0.01 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.

(20 pts)

Refer to the following data for Questions 28 and 29.

x 0 -1 3 5 y 3 -2 3 8

28. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. (15 pts)

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work and justify your answer. (5 pts)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 6 of 6

30. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.

Type 1 2 3 4

Number 30 24 22 24

Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are

equally popular? Justify your answer. (20 pts)