Download Practice Test 1

Name (Please Print) ___________________________
Class Times (Circle yours): 9:30 – 10:30 AM
1:30-2:20 PM
2:30 – 3:20 PM
STAT 350 (Practice) Exam 1
Following policies apply to the actual Exam:
You must have one sheet (double sided, 8” by 11”) of paper in
your own handwriting. That is counted as 1 pt. *
*Any violation, e.g. more than one pages, typed/copied page(s),
written by others, etc will be caught as cheating and reported.
Grade of 0 for the exam will be given as a punishment.
For multiple choice questions, please write the choice letter
ON THE LINE. (Unique answer for every multi-option Q)
For short-answer questions, please SHOW ALL YOUR WORK
to receive full credit.
When you finish your exam, attach your cheat sheet, submit
both to your instructor, sign the roster, and show your Purdue
I.D.
You are expected to uphold the Honor Code of Purdue
University. It is your responsibility to keep your work covered
at all times, you must not exchange anything during the exam.
All multiple choice questions are worth 4 points each.
Page
2
3
4
5
6
Points
Score
20
32
16
19
12
1
CheatSheet
1
Total
100
_______ 1. Which of the following statements regarding histograms is correct?
A) A unimodal histogram is one that rises to a single peak and then declines, whereas a
bimodal histogram is one that has two different peaks.
B) A unimodal histogram is positively skewed if the right or upper tail is stretched out
compared to the left or lower tail.
C) A unimodal histogram is negatively skewed if the left or lower tail is stretched out
compared to the right or upper tail.
D) A histogram is symmetric if the left half is a mirror image of the right half.
E) All of the above
_______ 2. Boxplots have been used successfully to describe
A) center of a data set
B) spread of a data set
C) the extent and nature of any departure from symmetry
D) identification of “outliers”, for modified Boxplots
E) All of the above
_______ 3. Let be the sample mean of a random sample of 16 observations, from a
population with mean of 72 and a standard deviation of 16. Then and  x are
A) 18 and 16, respectively
B) 18 and 1, respectively
C) 4 and 1, respectively
D) 72 and 2, respectively
E) 72 and 4, respectively
_______ 4. For any two events A and B, which of the following is always correct?
A) P(A or B) = P(A) + P(B)
B) P(A or B) = P( A)  P( B)
C) P(A or B) = P(A) + P(B) – P(A and B)
D) P(A and B) = P( A)  P( B)
E) P(A and B) = 0
_______ 5. The probability mass function of a discrete random variable x is defined as p(x) =
x/10 for x = 0, 1, 2, 3, and 4. Then, the probability that x is at most 3 is
A) .10
B) .30
C) .60
D) .90
2
_______ 6. Which of the following statements is true about a Poisson probability distribution
with parameter  ?
A) The mean of the distribution is 
B) The standard deviation of the distribution is 
C) The parameter  can be any real number.
D) All of the above statements are true
E) None of the above statements are true
_______ 7. A new car salesperson knows that he sells cars to one customer out of 20 who enter
the showroom. The probability that he will sell a car to exactly one of the next three
customers is
A) 0.1354
B) 0.0075
C) 0.0071
D) 0.8574
_______ 8. The number of tickets issued by a meter reader can be modeled by a Poisson
process with a rate parameter of six per hour. What is the probability that at least
three tickets are given out during a particular hour?
A) 0.5
B) 0.938
C) 0.0071
D) 0.875
_______ 9. The mean of a binomial distribution for which n = 25 and  = 0.20 is:
A) 125
B) 25
C) 20
D) 5
E) 4
_______ 10. For a uniform random variable on [0, 6], what’s the standard deviation?
A) 14
B) 18
C) 1.732
D) 3
E) None of A) to D)
_______ 11. If the probability density function of a continuous random variable x is
0 x2
.5 x
f ( x)  
otherwise
0
then P(1  x  1.5) is
A)
B)
C)
D)
.5625
.3125
.1250
.4375
A certain lake contains a large population of fish, half of which are salmon and the other half
trout. A team of wildlife experts randomly captures 100 of the fish to study. Use this story to
answer question 12 and 13.
_______ 12. What is the probability that the proportion of salmon in their sample is between 0.4
and 0.5? (Hint: Consider Normal approximation if that’s available)
A. 0.0793
B. 0.4772
C. 0.0000
D. 0.1508
______ 13. If the sample size is increased substantially, the probability that the sample
proportion is between 0.4 and 0.5 will be ____________ than your answer to question 11.
A. Larger
B. Smaller
C. Equal
D. Not sure.
3
________ 14. Suppose C and D are disjoint events, with P(C) = 0.3 and P(D) = 0.4. What is
P( C ' D ' ). “  ” indicates “or” relationship.
A.
B.
C.
D.
0.3
0.65
1.0
1.3
______ 15. A gambler enters a casino and plays a game in which he will lose $ 6.00 with
probability 1/3, win $ 2.00 with probability 1/2, and win $ 6.00 with probability 1/6. Let X = the
amount he wins after one play of the game. Then the expected value of his winnings is
A.
B.
C.
D.
$4.00
$2.00
$1.00
$0.00
16. (15 pts) Battery packs in electric go-carts need to be able to last a fairly long time. The runtimes (time until it needs to be recharged) of the battery packs made by a particular company are
normally distributed with a mean of 2 hours and a standard deviation of 20 minutes (1/3 hour).
a. (4 pts) How long do the bottom 15% of batteries last?
b. (4 pts) What is the probability that a battery will last between 100 and 140 minutes?
4
c. (4 pts) Now we randomly pick 4 packs of batteries from this company, what is the probability
that their mean run-time will be between 100 and 140 minutes?
d. (3 pts) Should we use Central Limit Theorem to solve part (c)? Interpret why or why not.
17. (12 pts) In a certain group of Purdue students, 50% drink alcohol, 30% smoke cigarettes,
15% drink alchohol and smoke cigarattes. A student is to be randomly selected from this group.
a. (8 pts) Draw a Venn diagram, with the sample space S, the events A=”the student drinks
alcohol” and B=”the student smokes cigarettes” all clearly labeled.
b. (4 pts) Are A and B independent? Why or why not? Please give clear reason.
18. (7 pts) It is known that 80% of all brand A zip drives work in a satisfactory manner
throughout the warranty period. Suppose that 25 drives are randomly selected. What is the
probability that less than 24 drives can work in a satisfactory manner in this sample?
Version A: USE Normal Approximation for Binomial distribution and continuity
correction to solve this problem. (i.e. Any other method will be graded as 0 evern if the
number is correct)
Version B: No specification, i.e. besides method in version A, you can choose to calculate the
“exact Binomial mass funtions”, or probability in terms of the sample proportion.
5
19. (5 pts) In a certain population, 1% of all individuals are carriers of a particular disease. A
diagnostic test for this disease has a 90% detection rate (with positive test results) for carriers and
a 5% detection rate for noncarriers. Suppose that the diagnostic test is applied to a random
selected individual. If the test is positive, what is the probability that the selected individual is a
carrier?
6
7
8
9
10