STAT 2300
Test #2 (Version B)
Spring 2017
Student's Printed Name: __________________________________
CUID:__________________
Lecture Instructor: ___________________________
Lecture Section # :________
You are permitted to use a calculator on all portions of this test. You are not allowed to use any notes,
textbooks, cell phones, or laptops on this test. All devices that can send and receive information
(including smart watches) must be turned off and put away while you are in the testing room.
During this test, any communication with any person (other than the instructor or test proctor) in any
form, including written, signed, verbal, or digital, is understood to be a violation of academic integrity.
No part of this test may be removed from the testing room.
Read each question very carefully. In order to receive full credit for the free response portion of the test,
you must:
1. Show legible and logical (relevant) justification which supports your final answer.
2. Use complete and correct mathematical notation.
3. Include proper units, if necessary.
You have 90 minutes to complete the entire test.
On my honor, I have neither given nor received inappropriate or unauthorized information at any
time before or during this test.
Student's Signature: ________________________________________________
Do not write below this line.
Free Response Problem Points Possible Points Earned
1
11
2
10
3
10
4
8
Free Response Total
39
Multiple Choice
60
Correct Scantron
1
Test Total
100
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STAT 2300
Test #2 (Version B)
Spring 2017
Part I: Multiple Choice. There are 20 multiple choice questions. Solve each question using the
available space for scratch work. Decide which is the best of the choices given and fill in the
corresponding oval on the provided scantron using a #2 pencil. For your own record, also circle your
choice on your test since the scantron will not be returned to you. Only the responses recorded on your
scantron sheet will be graded. Each multiple choice question is worth 3 points.
1. Which of the following is an example of a continuous random variable?
(A) The number of light bulbs that burn out in the next week in a large classroom
(B) The time it takes for a light bulb to burn out
(C) The brand name of each light bulb in a large classroom
(D) None of the above
2. The random variable X = weight of laboratory cockroaches follows a normal distribution with mean
80 grams and standard deviation 2 grams. The following figure is the normal curve for this
distribution of weights.
X
The shaded region of this graph has area 0.3023. Based on this information, which of the following
statements is true?
(A) P(75 ≤ X ≤ 79) = 0.3023
(B) P(75 < X < 79) = 0.3023
(C) Approximately 30% of all laboratory cockroaches will weigh between 75 and 79 grams
(D) All of the above are true
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STAT 2300
Test #2 (Version B)
Spring 2017
Use the following information to answer questions 3 – 4.
A large auto dealership keeps track of sales made during each hour of the day. Let X = the number of
cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the
probability distribution of X is as follows:
X
0
1
2
P(X)
0.3
0.5
0.2
3. Which of the following statements is NOT true?
(A) P(X > 0) = 0.7
(B) P(X > 1) = 0.7
(C) P(X ≤ 1) = 0.8
(D) P(X = 3) = 0
4. Calculate the standard deviation of X.
(A) 0.90
(B) 0.70
(C) 0.63
(D) 0.49
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STAT 2300
Test #2 (Version B)
Spring 2017
5. Find P(−0.97 < Z ≤ 1.72).
(A) 0.1660
(B) 0.7913
(C) 0.9573
(D) 0.9964
Use the following information for questions 6 – 7.
At an upstate appliance store, the probability that a person walking in will buy a washing machine is
0.023 and the probability that he or she will buy a dryer is 0.019. Also, if the person buys a washer, then
the probability that he or she will also buy a dryer is 0.216.
6. For a randomly selected customer, are the events "Buy a Washer" and "Buy a Dryer" independent?
(A) Yes; the probability of buying a washer and the probability of buying a dryer are both very small.
(B) No; a person is much more likely to buy a dryer if he or she is buying a washer.
(C) Yes; the probability of buying a washer and the probability of buying a dryer are almost equal.
(D) No; the probability of buying a washer and the probability of buying a dryer are not exactly equal.
7. Calculate the probability that a person will buy a washer and a dryer.
(A) 0.007
(B) 0.006
(C) 0.005
(D) 0.004
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STAT 2300
Test #2 (Version B)
Spring 2017
8. In which of the following situations would it be appropriate to use a normal distribution to
approximate probabilities for a binomial distribution with the given values of n and p?
(A) n = 100, p = 0.99
(B) n = 100, p = 0.2
(C) n = 50, p = 0.8
(D) n = 10, p = 0.5
9. A cereal company has found that the amount of cereal in a randomly selected box follows a normal
distribution with a mean of 18 ounces and a standard deviation of 0.2 ounces. One of the following
histograms displays the mean amount of cereal in 1000 samples of n = 5 boxes of cereal, and the
other displays the mean amount of cereal in 1000 samples of n = 25 boxes of cereal.
Graph I
Graph II
Which histogram is based on samples of n = 5 boxes of cereal? Explain.
(A) Graph I because as the sample size decreases variability in the sample means will increase
(B) Graph I because as the sample size decreases variability in the sample means will decrease
(C) Graph II because as the sample size decreases variability in the sample means will increase
(D) Graph II because as the sample size decreases variability in the sample means will decrease
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STAT 2300
Test #2 (Version B)
Spring 2017
10. If X is a random variable that follows a normal distribution with a mean of 10 and standard deviation
of 2.5, what value of X represents the 50th percentile?
(A) 11.25
(B) 10
(C) 2.5
(D) 0
11. José read an article that claimed 1 out of every 4 eggs contains salmonella bacteria. So, whenever he
cooks he never uses more than 3 eggs. Let X represent the number of contaminated eggs when José
uses 3 chosen at random. Assuming salmonella contamination is independent for any two eggs,
which of the following statements is correct?
(A) X is not a binomial random variable
(B) X is a binomial random variable with n = 3 and p = 13
(C) X is a binomial random variable with n = 3 and p = 14
(D) X is a binomial random variable with n = 4 and p = 14
12. Mark opens a fun size bag of Skittles candy containing 2 reds, 5 oranges, 3 yellows, 2 greens, and 3
purples. Mark's two favorites are the red candies and the purple candies. If he randomly selects two
Skittles from the bag without replacement, what is the probability that he will get exactly one red
and exactly one purple?
(A) 0.0286
(B) 0.0533
(C) 0.0571
(D) 0.1111
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STAT 2300
Test #2 (Version B)
Spring 2017
13. Consider the following normal probability plot for a random sample of n = 30 observations.
Is it reasonable to assume the data are from a population that is normally distributed?
(A) Yes because there is a curved pattern to the normal probability plot and some points fall outside
the curved bounds.
(B) No because there is a curved pattern to the normal probability plot and some points fall outside
the curved bounds.
(C) Yes because the normal probability plot is roughly linear and only a few points fall outside the
curved bounds.
(D) No because the normal probability plot is roughly linear and only a few points fall outside the
curved bounds.
14. Customers who register to bank online with Cambio Bank are issued a randomly generated password
that is 5 characters long, each of which can be one of the 26 lowercase letters of the alphabet, one of
the single digit numbers between 0 and 9, or one of these special characters: @, #, $, %. What is the
probability that one of these passwords does NOT contain any repeated characters?
(A) 0.771
(B) 0.766
(C) 0.015
(D) 0.006
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STAT 2300
Test #2 (Version B)
Spring 2017
15. The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps
throughout the state to detect the moths. Each month, a random sample of 50 traps is inspected, the
number of moths in each trap is recorded, and the mean number of moths is calculated. Based on
many years of data, the distribution of moth counts is extremely skewed right with a mean of 1.5 and
a standard deviation of 0.6. Describe the distribution of the sample mean number of moths for
samples of size 50.
(A) Approximately normal with a mean of 1.5 and a standard deviation of 0.6
(B) Approximately normal with a mean of 1.5 and a standard deviation of approximately 0.085
(C) Skewed right with a mean of 1.5 and a standard deviation of 0.6
(D) Skewed right with a mean of 1.5 and a standard deviation of approximately 0.085
16. The average speed of vehicles traveling on Interstate 85 between Anderson, SC and Greenville, SC
follows a normal distribution with a mean of 67 mph and a standard deviation of 3.5 mph. What
proportion of cars drive below the speed limit of 65 mph?
(A) 0.2843
(B) 0.4286
(C) 0.5714
(D) 0.7157
17. Find 𝑧𝑧0.37 .
(A) 0.64
(B) 0.36
(C) 0.33
(D) −0.33
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STAT 2300
Test #2 (Version B)
Spring 2017
18. Since Clemson won the 2016 college football championship, 6 out of 10 Clemson students have
purchased a commemorative shirt. Out of a random sample of 5 Clemson students, what is the
probability that none of them bought a shirt?
(A) 0.01
(B) 0.08
(C) 0.40
(D) 0.60
19. Twelve people have been exposed to a particular disease. Each one independently has a 40% chance
of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the
probability that the hospital's capacity will be exceeded?
(A) 12 C10 (0.4)10 (0.6)2 + 12 C11 (0.4)11 (0.6)1 + 12 C12 (0.4)12 (0.6)0
(B) 12 C10 (0.6)10 (0.4)2 + 12 C11 (0.6)11 (0.4)1 + 12 C12 (0.6)12 (0.4)0
(C) 12 C11 (0.4)11 (0.6)1 + 12 C12 (0.4)12 (0.6)0
(D) 12 C11 (0.6)11 (0.4)1 + 12 C12 (0.6)12 (0.4)0
20. A professor in the Math department is teaching two classes, one that meets at 8AM and one that
meets at 9AM. There are 35 students between these two classes: 13 students in the 8AM class only,
17 students in the 9AM class only, and 5 students in both the 8AM and 9AM classes. The professor
plans to randomly select one of his 35 students to receive a free calculator. Given that the selected
student is in the 9AM class, what is the probability that the selected student is also in the 8AM class?
(A) 0.143
(B) 0.227
(C) 0.278
(D) 0.294
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STAT 2300
Test #2 (Version B)
Spring 2017
Part II: Free Response. Show all your work. Indicate clearly the methods you use, because you will be
graded on the correctness of your methods as well as on the accuracy and completeness of your results
and explanations. Answers with no justification will receive no credit.
1. The table below gives a breakdown of the blood types for a random sample of 1,000 American
adults by letter (O, A, B, AB) as well as the presence of the Rh factor (+, −).
O
A
B
AB
Total
Rh +
380
340
90
30
840
70
60
20
10
160
Total
450
400
110
40
1,000
Rh −
One of these American adults is randomly selected. For the questions below, label your answers
with appropriate probability notation, using the category name to denote the event the randomly
selected person is in that category. Show your calculations and answer with a fraction or a
decimal rounded to two decimal places.
(a) What is the probability that the person selected has Rh + blood? (2 pts)
(b) What is the probability that the person selected has Rh + or type O blood? (3 pts)
(c) If we know that the person selected has type AB blood, what is the probability that he or she has
Rh + blood? (3 pts)
(d) Are the events AB and Rh + independent? Justify your answer. (3 pts)
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STAT 2300
Test #2 (Version B)
Spring 2017
2. Some companies, such as DemandTec, have developed software to help retail chains set prices that
optimize their profits. An Associated Press story (April 28, 2007) about this software described a
case in which a retail chain sold three similar power drills: one for $80, a better one for $110, and a
top-tier one for $140. Software predicted that by selling the middle-priced drill for only $100, the
cheaper drill would seem like less of a bargain and more people would buy the middle-priced drill.
(a) For the original pricing, suppose 50% of the sales were for the $80 drill, 20% for the $110 drill,
and 30% for the $140 drill. If we let X = the selling price for the sale of a drill under the original
pricing plan, then the table below gives the probability distribution of X.
X
$80
$110
$140
P(X)
0.5
0.2
0.3
Find the expected value of X. (3 pts)
(b) Interpret the expected value that you calculated in part (a). (3 pts)
(c) For the new pricing, suppose 30% of sales were for the $80 drill, 40% for the $100 drill, and
30% for the $140 drill. Is the expected selling price higher with this new pricing strategy?
Explain your answer and show any relevant calculations. (4 pts)
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STAT 2300
Test #2 (Version B)
Spring 2017
3. The graph below is a probability histogram for X, the total number of dogs and cats owned per
household, for the households in a large suburban area.
(a) According to an antiquated local law, each household in this area is prohibited from owning
more than 3 of these pets. If a household in this area is selected at random, what is the
probability that the selected household will be in violation of this law? Show all of your
calculations and label your answer with appropriate probability notation. (2 pts)
(b) If 10 households in this area are selected at random, what is the probability that exactly 1 of them
will be in violation of this law? Show all of your calculations and label your answer with
appropriate probability notation. Round your answer to four decimal places. (4 pts)
(c) The mean and standard deviation of X are 1.65 and 1.851, respectively. Suppose 150 households
in this area are to be selected at random and 𝑥𝑥̅ , the mean number of dogs and cats per household,
is to be computed. What is the probability that 𝑥𝑥̅ will be greater than 2? Show all of your
calculations and label your answer with appropriate probability notation. (4 pts)
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STAT 2300
Test #2 (Version B)
Spring 2017
4. The summer monsoon rains in India follow an approximately normal distribution with mean 852 mm
of rainfall and standard deviation 82 mm.
(a) Unusually high rainfall is considered to be more than 1022 mm of rain. What proportion of years
experience unusually high rainfall? Show all of your work and label your answer with
appropriate probability notation. (4 pts)
(b) How much rainfall was there if a given year is at the 10th percentile? Show all of your work and
label your answer with appropriate probability notation. (4 pts)
____________________________________________________________________________________
Did you correctly fill in your scantron? (1 pt)
 Did you write your name, lecture section #, and lecture instructor at the top of the form?
 Did you fill in your CUID with the C bubbled as a 0?
 Did you bubble in your Test Version?
 Are your bubbles filled in dark enough so that the form can be machine read?
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