BCC Math 2 Final Exam Form 328Fall 2022

Professor Yuan

Name ___________________________________

I, the undersigned, promise that this is work of my own understanding and am not receiving any

outside help whatsoever. If requested, I agree to a zoom interview with Professor Yuan in order to

verify that I can explain everything I submitted in full details, plus all peripheral and related topics,

as well as demonstrating similar problems, or receive zero points on this exam.

Signature ___________________________________

(This exam will not be graded without name and signature. You will submit the exam on your own sheets of paper, but you

must include this page, or copy the statement in exact wording above, with name and signature, or it will not be graded.)

Correct answers are worth zero points on this exam. Detailed, step-by-step work, calculations, and/or explanations that

leads to the answer(s) from the beginning are credited according to the extent of accuracy and completeness. If Step 1 does

not lead to Step 2, then all subsequent steps are not credited, even if the answer is correct. Your work and explanations must

be clear, logical, detailed and complete.

Form ID must match the exam you are assigned for full credit. Work as required should be done on separate sheets of paper.

All work must be clearly labeled and legible. Answer with no work or insufficient work will receive no credit on that

problem. Partial credit may be given. Remember – CORRECT ANSWERS ONLY, OR WORK DONE BY OTHERS, ARE

WORTH ZERO POINTS!

(*Cheating and plagiarism also subject you to further disciplinary actions from the college.)

All pages of the exam must be submitted from the same email address, to cyuan@barstow.edu, before 11:59 pm 12/15/2022,

Pacific Time.

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your

answer to the same number of decimal places as the sample mean.

1) 37 packages are randomly selected from packages received by a parcel service. The sample

1)

has a mean weight of 10.3 pounds and a standard deviation of 2.4 pounds. What is the 95%

confidence interval for the true mean weight, µ, of all packages received by the parcel

service?

Use the given information to find the minimum sample size required to estimate an unknown population mean µ.

2) How many students must be randomly selected to estimate the mean weekly earnings of

2)

students at one college? We want 95% confidence that the sample mean is within $2 of the

population mean, and the population standard deviation is known to be $60.

1

Solve the problem.

3) A local newspaper claims that 70% of the items advertised in its classifieds section are sold

within 1 week of the first appearance of the ad. To check the validity of the claim, the

newspaper randomly selected n = 25 advertisements from last year’s classifieds and

contacted the people who placed the ads. They found that 14 of the 25 items sold within a

week. Based on the newspaper’s claim, is it likely to observe x 14 who sold their item

within a week? Use a binomial probability table.

4) The scores on a certain test are normally distributed with a mean score of 60 and a

standard deviation of 5. What is the probability that a sample of 90 students will have a

mean score of at least 60.527?

3)

4)

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

5) Of 380 randomly selected medical students, 21 said that they planned to work in a rural

5)

community. Find a 95% confidence interval for the true proportion of all medical students

who plan to work in a rural community.

Solve the problem.

6) How much money does the average professional football fan spend on food at a single

football game? That question was posed to ten randomly selected football fans. The

sampled results show that the sample mean and sample standard deviation were $70.00

and $17.50, respectively. Use this information to create a 95 percent confidence interval for

the population mean.

Find the indicated probability. Round to three decimal places.

7) A machine has 11 identical components which function independently. The probability

that a component will fail is 0.2. The machine will stop working if more than three

components fail. Find the probability that the machine will be working.

Solve the problem.

8) Parking at a university has become a problem. University administrators are interested in

determining the average time it takes a student to find a parking spot. An administrator

inconspicuously followed 100 students and recorded how long it took each of them to find

a parking spot. Identify the population of interest to the university administration.

9) In the game of Parcheesi each player rolls a pair of dice on each turn. In order to begin the

game, you must roll a five on at least one die, or a total of five on both dice. Find the

probability that the player does not get to begin the game on either the first or the second

rolls.

2

6)

7)

8)

9)

10) The overnight shipping business has skyrocketed in the last ten years. The single greatest

predictor of a company’s success is customer service. A study was conducted to determine

the customer satisfaction levels for one overnight shipping business. In addition to the

customer’s satisfaction level, the customers were asked how often they used overnight

shipping. The results are shown below in the following table:

Frequency of Use

< 2 per month
2 - 5 per month
> 5 per month

TOTAL

High

250

140

70

460

Satisfaction level

Medium

140

55

25

220

Low

10

5

5

20

10)

TOTAL

400

200

100

700

A customer is chosen at random. Given that the customer uses the company less than two

times per month, what is the probability that the customer expressed low satisfaction with

the company?

11) Suppose that 62% of the employees at a company are male and that 35% of the employees

just received merit raises. If 20% of the employees are male and received a merit raise,

what is the probability that a randomly chosen employee is male or received a merit raise?

11)

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the

given statistics and confidence level. Round the margin of error to four decimal places.

12) In a clinical test with 1600 subjects, 800 showed improvement from the treatment. Find the

12)

margin of error for the 99% confidence interval used to estimate the population proportion.

Solve the problem.

13) Many track runners believe that they have a better chance of winning if they start in the

inside lane that is closest to the field. For the data below, the lane closest to the field is Lane

1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the

starting positions for the winnners of 240 competitions. Calculate the chi-square test

statistic 2 used to test the claim that the probability of winning is the same regardless of

13)

starting position..

Starting Position

Number of Wins

1 2 3 4 5 6

44 33 36 45 32 50

14) A recent article in the paper claims that business ethics are at an all-time low. Reporting on

a recent sample, the paper claims that 37% of all employees believe their company

president possesses low ethical standards. Suppose 20 of a company’s employees are

randomly and independently sampled. Assuming the paper’s claim is correct, find the

probability that more than eight but fewer than 12 of the 20 sampled believe the company’s

president possesses low ethical standards. Round to six decimal places.

3

14)

15) You are interested in purchasing a new car. One of the many points you wish to consider is

the resale value of the car after 5 years. Since you are particularly interested in a certain

foreign sedan, you decide to estimate the resale value of this car with a 99% confidence

interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the

same model. These 17 cars were resold at an average price of $12,760 with a standard

deviation of $700. Suppose that the interval is calculated to be ($12,264.09, $13,255.91).

How could we alter the sample size and the confidence coefficient in order to guarantee a

decrease in the width of the interval?

Solve the problem.

16) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the

company gets complaints that their bottles are not holding enough liquid. To test this

claim, the bottling company randomly samples 24 bottles and finds the average amount of

liquid held by the bottles is 9.8 ounces with a standard deviation of .3 ounce. Calculate the

appropriate test statistic.

15)

16)

17) An automobile manufacturer has determined that 30% of all gas tanks that were installed

on its 2002 compact model are defective. If 9 of these cars are independently sampled, what

is the probability that more than half need new gas tanks?

17)

18) A machine has four components, A, B, C, and D, set up in such a manner that all four parts

must work for the machine to work properly. Assume the probability of one part working

does not depend on the functionality of any of the other parts. Also assume that the

probabilities of the individual parts working are P(A) = P(B) = 0.92, P(C) = 0.9, and P(D) =

0.98. Find the probability that the machine works properly.

18)

19) According to a recent study, 1 in every 7 women has been a victim of domestic abuse at

some point in her life. Suppose we have randomly and independently sampled

twenty-five women and asked each whether she has been a victim of domestic abuse at

some point in her life. Find the probability that at least 2 of the women sampled have been

the victim of domestic abuse. Round to six decimal places.

19)

20) In a certain population, body weights are normally distributed with a mean of 152 pounds

and a standard deviation of 26 pounds. How many people must be surveyed if we want to

estimate the percentage who weigh more than 180 pounds? Assume that we want 96%

confidence that the error is no more than 4 percentage points.

20)

21) Suppose a basketball player is an excellent free throw shooter and makes 90% of his free

throws (i.e., he has a 90% chance of making a single free throw). Assume that free throw

shots are independent of one another. Find the probability that the player misses three

consecutive free throws.

21)

22) Explain why the following is or is not a valid probability distribution for the discrete

random variable x.

22)

x

p(x)

0

-.1

2

.1

4

.2

6

.3

8

.5

4

Solve the problem. Round to four decimal places.

23) If x is a binomial random variable, compute p(x) for n = 6, x = 3, p = 0.5.

Solve the problem.

24) Fifteen SmartCars were randomly selected and the highway mileage of each was noted.

The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per

gallon. Which of the following would represent a 90% confidence interval for the average

highway mileage of all SmartCars?

25) Each manager of a corporation was rated as being either a good, fair, or poor manager by

his/her boss. The manager’s educational background was also noted. The data appear

below:

Educational Background

Manager

Rating H. S. Degree Some College College Degree Master’s or Ph.D. Totals

Good

9

2

27

1

39

Fair

5

12

47

23

87

Poor

4

7

3

20

34

Totals

18

21

77

44

160

What is the probability that a randomly chosen manager is either a good managers or has

an advanced degree?

5

23)

24)

25)

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