Barstow Community College Mathematics Worksheet

BCC Math 2 Final Exam Form 328Fall 2022
Professor Yuan
Name ___________________________________
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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.
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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)