Practice Midterm II
Printable Key
Problem 1
The South Lake Tahoe Police Department has charted the number of arrests over the past twelve
months. The number of arrests per month that are made follows a Normal distribution with
mean
72
and standard deviation
12
. Construct a control chart and determine any out of control
signals.
Month
1
2
3
4
5
6
7
8
9
10
11
12
Arrests
61
74
73
98
76
80
110
75
81
100
51
40
Solution
Problem 2
Stellar Jay hatchlings have a body weight that is approximately normally distributed with a mean
of
3.4
ounces and a standard deviation of
0.3
ounces.
A. Convert the following xintervals into zintervals.
x > 3.0 x < 6.0
Solution
B. Convert the following zinterval into an xinterval
1.2 < z < 0.6
Solution
Problem 3
Your tire company's snow and mud tires have an average lifetime of
80,000
miles with a
standard deviation of
10,000
miles. Answer the following assuming the distribution is normal.
A. If the current guarantee for the tires is
65,000
miles, about what percentage of the tires will
wear out before the guarantee expires?
Solution
B. You want to reconsider the guarantee so that about
98%
last past the guarantee period. What
should you set as the guarantee period on your tires?
Solution
Problem 4
The Lake Tahoe Visitor's Authority has determined that
65%
of the tourists who come to the
Lake Tahoe area to go snowboarding are from the Bay area. The Boarder Motel has all of its
35
rooms booked during this weekend.
A. What is the probability that between
20
and
25
of the rooms host bay area visitors?
Solution
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View Full DocumentB. Why is your estimate valid?
Solution
Problem 5
Explain what the difference is between a sampling distribution and the distribution of a sample.
Solution
Problem 6
It is know that the mean number of houses a TrickOrTreater visits is
46
and the standard
deviation is
8
.
A. Assuming that the distribution is approximately normal, what is the probability that your
seven year old neighbor will visit fewer than
42
houses on Halloween?
Solution
B.
25
children were randomly selected and observed. What is the probability that their mean
number of visits is between
48
and
55
?
Solution
Problem 7
Do you favor allowing pilots to carry a gun in the cockpit?
74%
of Americans are in favor of
allowing pilots to carry a gun in the cockpit.
A.
80
passengers board a plane heading toward New York. What is the probability that the
greater than
75%
of them favor allowing the pilot to carry a gun?
Solution
B. Is the normal approximation to the proportion
p = r/n
valid? Explain.
Solution
Problem 8
The manager of Wasabi restaurant tallied the number of customers that he received over a
50
day
period. He found that the mean number per day for this period was
45
with a standard deviation
of 8. Construct a
95%
confidence interval for the true mean. Write a sentence that explains your
findings.
Solution
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 Spring '10
 Driscoll
 Statistics, Normal Distribution, Standard Deviation, Sierra Nevada Mountains

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