AP Statistics
Review Packet 2012
Mr. Dooley
Name:__________________________________
1.) A company is considering implementing one of two quality control plans for monitoring the
weights of automobile batteries that it manufactures. If the manufacturing process is working properly,
the battery weights are approximately normally distributed with a specified mean and standard
deviation.
Quality control plan A calls for rejecting a battery as defective if its weight falls more than 2 standard
deviations below the specified mean.
Quality control plan B calls for rejecting a battery as defective if its weight falls more than 1.5
interquatile ranges below the lower quartile of the specified population.
Assume the manufacturing process is working properly.
(a) What proportion of batteries will be rejected by plan A?
(b) What proportion of batteries will be rejected by plan B?
3) The Better Business Council of a large city has concluded that students in the city’s schools are not
learning enough about economics to function in the modern world. These findings were based on test
results from a random sample of 20 twelfth-grade students who completed a 46 question multiple
choice test on basic economic concepts. The data set below shows the number of questions that each
of the 20 students in the sample answered correctly.
12
43
16
8
18
16
17
14
18
10
33
9
41
44
38
35
19
36
19
(a) Display these data in a stemplot.
(b) Use your stemplot from part (a) to describe the main features of this score distribution.
(c) Why would it be misleading to report only a measure of center for this score distribution?
13
3.) A professional sports team evaluates potential players for a certain position based on two main
characteristics, speed and strength.
(a) Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating more
desirable (faster) speeds. From previous speed data for all players in this position, the times to run 40 yards have
a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of 4.40 seconds, as
shown in the table below.
Time to run 40 yards
Mean
4.60 seconds
Standard Deviation
0.15 seconds
Minimum
4.40 seconds
Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to believe
that the distribution of 40-yard running times is approximately normal? Explain.
(b) Strength is measured by the amount of weight lifted, with more weight indicating more desirable (greater)
strength. From previous strength data for all players in this position, the amount of weight lifted has a mean of
310 pounds and a standard deviation of 25 pounds, as shown in the table below.
Amount of weight lifted
Mean
310 pounds
Standard Deviation
25 pounds
Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.
(c) The characteristics of speed and strength are considered to be of equal importance to the team in selecting a
player for the position. Based on the information about the means and standard deviations of the speed and
strength data for all players and the measurements listed in the table below for Players A and B, which player
should the team select if the team can only select one of the two players? Justify your answer.
Time to run 40 yards
Amount of weight lifted
Player A
4.42 seconds
370 pounds
Player B
4.57 seconds
375 pounds
4.) Hurricane damage amounts, in millions of dollars per acre, were estimated from insurance records
for major hurricanes for the past three decades. A stratified random sample of five locations (based
on categories of distance from the coast) was selected from each of three coastal regions in the
southeastern United States. The three regions were Gulf Coast (Alabama, Louisiana, Mississippi),
Florida, and Lower Atlantic (Georgia, South Carolina, North Carolina). Damage amounts in
millions of dollars per acre, adjusted for inflation, are shown in the table below.
Gulf Coast
Florida
Lower Atlantic
< 1 mile
24.7
35.1
21.8
Distance from Coast
1 to 2 miles
2 to 5 miles
21.0
12.0
37.1
20.7
15.7
12.6
5 to 10 miles
7.3
6.4
1.2
10 to 20 miles
1.7
3.0
0.3
(a) Sketch a graphical display that compares the hurricane damage amounts per acre for the three
different coastal regions (Gulf Coast, Florida, and Lower Atlantic) and that also shows how the
damage amounts vary with distance from the coast.
(b) Describe differences and similarities in the hurricane damage amounts among the three regions.