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AP Statistics
First 6 Week Review
Name ________________
1. In a study of how college students give directions from maps, 40 Introductory Psychology volunteers, 20 men and 20
women, were given the task of giving directions to another. Observations were made of subjects' direction-giving
behavior in the experiment:
(a) whether the map was available, or the directions were given from memory,
(b) the sex of the direction giver,
(c) the distances given as part of the directions,
(d) the number of times directions such as North, Southwest, etc. were used, and
(e) the frequency of errors in the directions
For each of the variables in this experiment, determine whether it is categorical or numerical. For each numerical
variable, determine whether it is discrete or continuous.
2. According to the Internet Movie Data-base, Avatar is tops based on box office sales worldwide.
The following table displays data on several popular movies
Movie
Year
Rating
Time
Genre
Box office
Avatar
2009
PG-13
162
Action
2,714,767,458
Titanic
1997
PG-13
194
Drama
1,835,300,000
2003
PG-13
201
Action
1,129,219,252
2006
PG-13
151
Action
1,060,332,628
2008
PG-13
152
Action
1,001,921,825
The Lord of the Rings: Return of the
King
Pirates of the Caribbean: Dead
Man’s Chest
The Dark Knight
A. What individuals does this data set describe?
B. Clearly identify each of the variables. Which are quantitative? In what units do you think they are measured?
3. Bat characteristics: Biologists know that bats have different flight characteristics. Some bats exhibit fast, straight,
and long flights; others are moderately slow, and highly maneuverable. The flight capabilities of bats are presumably a
function of (a) the characteristics of the bat wings, and (b) the laws of physics. The data presented below are wing
spans in centimeters for certain species of bats from Nicaragua and Costa Rica. Two categories of bat species are
represented: fruit-eaters and insect-eaters.
Fruit eaters:
25.2, 27.2, 42.0, 44.8, 31.3, 32.5, 32.0, 28.1, 30.7, 27.0, 41.1, 41.6, 58.4, 58.7, 53.9
Insect eaters:
32.8, 27.4, 21.0, 23.9, 27.5, 22.4, 18.7
a) Construct back to back stem plots that will allow you to easily compare the distributions of the wing spans for the
two categories of bats, fruit-eaters and insect-eaters.
b) Write a short paragraph describing the features of the two plots; what do these plots tell you about the differences
in wing span for fruit- and insect-eaters?
4. Here are the survival times in days of 72 guinea pigs after they were injected with
infectious bacteria in a medical experiment. Survival times, whether of machines under stress or cancer patients
after treatment, usually have distributions that are skewed to the right.
43
80
91
103
137
191
45
80
92
104
138
198
53
81
92
107
139
211
56
81
97
108
144
214
56
81
99
109
145
243
57
82
99
113
147
249
58
83
100
114
156
329
66
83
100
118
162
380
67
84
101
121
174
403
73
88
102
123
178
511
74
89
102
126
179
522
79
91
102
128
184
598
Make a histogram of the data on the calculator and describe its main features.(SOCS) Does it show the
expected right-skew?
5. A sample of 11 U.S. families spent the following amounts (in dollars) on groceries during a
one-week period:
$39.92, $31.72, $60.16, $21.55, $13.35, $21.12, $24.38, $43.52, $51.64, $35.34, $27.73
Find the mean, median and standard deviation. Write a statement interpreting this data
in context.
6. Birth weights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15
oz. Find the proportion of infants with birth weights between
125 oz. and 140 oz.
7. The risk of an investment is measured by the variability of the changes in its value over a fixed period, such as a
year. More variation from year to year means more risk. The government's Securities and Exchange Commission
wants to require mutual funds to tell investors how risky they are. A news article (New York Times, April 2, 1995)
says that some people think that "the proposed risk descriptions, especially one that goes by the daunting name
standard deviation" are hard to understand. Explain to a friend what the standard deviation means, using the fact
that the changes in a mutual fund's value over many years have a roughly normal distribution.
8. A lunch stand in the business district has a mean daily gross income of $420 with a
standard deviation of $50. Assume that the daily gross income is normally distributed.
A. If a randomly selected day has a gross income of $520, then how many standard deviations away from the mean
is that day’s gross income?
B. Determine the standardized value for the daily income of $520.
C. What is the relative frequency corresponding to a daily gross income of $520 or more?
9. Find the proportion of observations from a standard normal distribution that satisfies each of
the following statements. DRAW the scenario.
A. Z < –2.25
B. –2.25 < Z < 1.7
10. Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year
period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard deviation of 511
grams. Babies that weigh less than 2500 grams at birth are classified as “low birth weight.”
A. What percent of babies will be identified as low birth weight? Show your work.
B. Find the quartiles of the birth weight distribution.
11. Mr. Walker measures the heights (in inches) of the students in one of his classes. He uses a
computer to calculate the following numerical summaries:
Mean
Std. dev.
Min
Q1
M
Q3
Max
69.188
3.20
61.5
67.75
69.5
71
74.5
Next, Mr. Walker has his entire class stand on their chairs, which are 15 inches off the ground.
Then he measures the distance from the top of each student’s head to the floor.
A. Find the mean and median of these measurements.
B. Find the standard deviation and IQR of these measurements.
12. The distribution of weights of 9-ounce bags of a particular brand of potato chips is
approximately Normal with mean µ = 9.12 ounces and standard deviation σ = 0.05 ounce.
A. What percent of bags weigh less than 9.02 ounces?
B. Between what weights do the middle 68% of bags fall?
C. What percent of 9-ounce bags of this brand of potato chips weigh between 8.97 and 9.17 ounces?
D. A bag that weighs 9.07 ounces is at what percentile in this distribution?
13. The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and
standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends
more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and
standard deviation of this distribution.