Name________________________
Math 232
Practice Exam 2
You can use StatCrunch for this exam. Looking at anything else on your computer will be considered
cheating. For each of the following, please show all your work. Simplify fully. Write a complete
sentence with proper grammar when asked for an interpretation. Unless stated otherwise, each problem is
worth 4 points. Unless stated otherwise, round to 3 decimal places.
Deduction for work done in pen or for work that is hard to follow:_______(up to 2 points).
Warning: Other types of problems might appear on the actual test.
1) Open up data set 4_2_29 in StatCrunch to view data on houses.
a) Compute the linear correlation coefficient r.
b) The correlation coefficient from (a) indicates that there is a _________("strong" or "weak")
___________("positive" or "negative") association between the two variables.
c) Compute the regression line. Round each constant to 2 decimal places.
2) You are interested in Ford Mustangs. Let x = age (in years) of a Ford Mustang and y = price (in
dollars) of a Ford Mustang. Suppose that the regression equation is
,
.
a) Interpret the y-intercept of the regression equation or state that the interpretation would not be
appropriate. You must have a complete sentence with proper grammar.
b) Interpret the slope of the regression equation. You must have a complete sentence with proper
grammar.
c) Estimate the cost of a 4-year-old Mustang.
d) If the observed cost of a 4-year-old Mustang was $11,500, compute the residual.
3) a) Suppose
b) Given that
,
, and
, find
. Find
.
4) 2 fair dice are to be tossed.
a) Find the probability that the sum is 5. Round to 2 decimal places.
b) Find the probability that the sum is 12. Round to 2 decimal places.
5) Shale and sandstone are examples sedimentary rocks. A bag contains 15 pieces of shale and 8
pieces of sandstone. One rock will be drawn from the bag and set aside. Then a second rock will
be drawn from the bag. Find the probability that the first is shale and the second is sandstone.
6) I will flip a fair coin 5 times. Compute the probability that I get at least one tails.
7) The following data shows the worldwide reported shark attacks during the 1990s.1
Country
Australia (C1)
Brazil (C2)
South Africa (C3)
United States (C4)
Other (C5)
Total
Fatal
(L1)
9
12
8
5
36
70
Lethality
Nonfatal
(L2)
56
21
57
244
92
470
Total
65
33
65
249
128
540
a) Compute the probability that a reported shark attack occurred in the United States.
b) Compute the probability that a reported shark attack is fatal, given that it occurred in Brazil.
1
Source: International Shark Attack File, maintained by the American Elasmobranch Society and the Florida
Museum of Natural History. Cited in Weiss, Robert. Introductory Statistics (8th edition). San Francisco: Pearson,
2008. Pg. 195.
8) 200 independent flights are selected at random. Each flight has a 0.82 probability of arriving on
time. Find the probability that at least 160 will arrive on time.
9)
[6.1 #25] A life insurance company sells a $250,000 1-year term life insurance policy to a 20year-old female for $200. According to the National Vital Statistics Report, 58(21), the
probability that the female survives the year is 0.999544. Compute and interpret the expected
value of this policy to the insurance company.
Expected value:
Interpretation (in a complete sentence):
10) a) Compute the standard deviation of the following distribution. Round to 2 decimal places.
Hint: you will first have to compute the mean.
x
P(x)
10
0.7
50
0.3
b) Compute the standard deviation of a binomial distribution with 30 trials and a probability of
success of 0.71. Round to 2 decimal places.