AP Statistics Midterm Version A
1.) If a distribution is skewed to the right, which of the following is true?
A. The mean must be less than the median.
B. The mean and median must be equal.
C. The mean must be greater than the median.
D. The mean is either equal to or less than the median,
E. It’s impossible to tell which of the above statements is true without seeing the data.
2.) At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey
that asks for their age, area code, the number of years they have lived at their current address, their favorite school
subject, and whether they plan to go to college after high school. Which of the following best describes the
variables that are being measured?
A. four quantitative variables
B. five quantitative variables
C. two categorical variables and two quantitative variables
D. two categorical variables and three quantitative variables
E. three categorical variables and two quantitative variables
3.) The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches
and a standard deviation of 2.5 inches. About 32% of young men have heights outside the range
A. 65.5 inches to 70.5 inches
B. 63 inches to 73 inches
C. 60.5 inches to 75.5 inches
D. 58 inches to 78 inches
E. none of the above
4.) Use the information in the previous problem. About what percentage of the men are between 63 and 70.5 inches
tall? USE THE EMPERICAL RULE NOT Z-Score!
A. 81.2
B. 81.5
C. 81.85
D. 84
E.68
5.) Which of the following properties is true for all Normal density curves?
I. They are symmetric.
II. The curve reaches its peak at the mean.
III. 95% percent of the area under the curve is within one standard deviation of the mean.
A. I only
B. II only
C. I and II only D. I and III only E. All three statements are correct.
6.) Kitchen appliances don’t last forever. The lifespan of all microwave ovens sold in the United States is
approximately Normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage
of the ovens last more than 10 years?
A. 11.5%
B. 34.5%
C. 65.5%
D. 69%
E. 84.5%
7.) 11. A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the
number of service calls in a month y at each location. Summary calculations give
= 8.4,
= 2.1,
= 14.2,
= 3.8, and r = 0.82. About what percent of the variation in the number of service calls is explained by the linear
relation between number of service calls and number of machines?
A. 86%
B. 93%
C. 74%
D. 67%
E. Can’t tell from the information given
8.) We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the
households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is
11362
35692
96237
90842
46843
62719
64049
17823
Then the households selected are
A. households 11 13 36 62 73
B. households 11 36 23 08 42
C. households 11 36 23 23 08
D. households 11 36 23 56 92
E. households 11 35 96 90 46
9.) A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in a large
forest. There are too many trees to list them all and take a SRS, so he divides the forest into several hundred 10
meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every Sugar Maple in each one.
This is an example of a
A. multistage sample.
B. stratified sample.
C. simple random sample.
D. cluster sample.
E. convenience sample.
10.) To test the effects of a new fertilizer, a company took 100 plots. Fertilizer A is randomly applied to 50 of the
plots, and B to the other 50. This is
A. an observational study.
B. a matched pairs experiment.
C. a completely randomized experiment.
D. a block design, but not a matched pairs experiment.
E. not enough information
Scenario 5-13
The two-way table below gives information on seniors and juniors at a high school and by which means they
typically get to school.
Car
Bus
Walk
Totals
Juniors
146
106
48
300
Seniors
146
64
40
250
Totals
292
170
88
550
11.) Use Scenario 5-13. You select one student from this group at random. What is the probability that this student
typically takes a bus to school?
A. 0.256
B. 0.309
C. 0.353
D. 0.455
E. 0.604
12.) Use Scenario 5-13. You select one student from this group at random. If the student says he is a junior, what is
the probability that he walks to school?
A. 0.073
B. 0.160
C. 0.455
D. 0.600
E. 0.833
13.) If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?
A. 0.1248
B. 0.28
C. 0.6352
D. 0.76
E. The answer cannot be determined from the information given.
14.) There are 10 red marbles and 8 green marbles in a jar. If you take three marbles from the jar (without
replacement), the probability that they are all red is:
A. 0.069
B. 0.088
C. 0.147
D. 0.444
E. 0.171
15.) Which of the following is a true statement?
A. The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting
permits more than two outcomes.
B. A geometric random variable takes on integer values from 0 to n.
C. If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X
will be skewed left, since 0.85 is closer to 1 than to 0.
D. An important difference between binomial and geometric random variables is that there is a fixed number of
trials in a binomial setting, and the number of trials varies in a geometric setting.
E. The distribution of every binomial random variable is skewed right.
It has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause
illness if improperly cooked. Chickens are delivered to grocery stores in crates of 24. Assume the chickens are
independently selected for inclusion in the crate.
16. Use Scenario 6-11. The probability that a certain crate has 4 or more contaminated chickens is
A. 0.0424
B. 0.0686
C. 0.8889
D. 0.9313
E. 0.9576
17. The mean and standard deviation of the number of contaminated chickens in a crate are
A. 7; 2.24
B. 7; 2.68
C. 7;  = 5.04
D. 7.2; 2.24
E. 7.2; 5.04
18.) The following is a chart on the number of ounces of alcohol (one ounce is about 30 mL) consumed per week in
a sample of 150 students.
A study wished to classify the students as “light”, “moderate”, “heavy” and “problem” drinkers by the amount
consumed per week. About what percentage of students are moderate drinkers, that is consume between 4 and
16 ounces per week?
(a) 60%
(b) 20%
(c) 40%
(d) 80%
(e) 50%
19.) “Normal” body temperature varies by time of day. A series of readings was taken of the body temperature
of a subject. The mean reading was found to be 36.5° C with a standard deviation of 0.2° C. When converted
to °F, the mean and standard deviation are
(°F = °C(1.8) + 32).
(a)
(b)
(c)
(d)
(e)
97.7, 0.36
97.7, 0.30
97.7, 0.54
97.7, 0.97
97.7, 1.80
20.) The following is a histogram showing the actual frequency of the closing prices on the New York exchange
of a particular stock. Based on the frequency histogram for New York Stock exchange, the class that
contains the 30th percentile is:
(a) 20-30
(b) 10-20
(c) 40-50
(d) 50-60
(e) 30-40
21.) There are three children in a room, ages three, four, and five. If a 6-year-old child enters the room the
(a)
(b)
(c)
(d)
(e)
mean age will stay the same but the variance will increase.
mean age will stay the same but the variance will decrease.
mean age and variance will stay the same.
mean age and variance will increase.
mean age and variance will decrease.
22.) The weights of the male and female students in a class are summarized in the following boxplots:
Which of the following is NOT correct?
(a) About 50% of the male students have weights between 150 and 185 pounds.
(b) About 75% of female students have weights more than 130 pounds.
(c) The median weight of male students is about 162 pounds.
(d) The mean weight of female students is about 120 pounds because of symmetry.
(e) The female students have less variability than the male students.
23.) The area under the standard normal curve corresponding to –0.45<Z<1.6 is
(a) 0.6188
(b) 0.4713
(c) 0.5631
(d) 0.9542
(e) None of the above
24.) In a statistics course, a linear regression equation was computed to predict the final exam score from the score
on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test.
Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
(a) 95
(b) 85.5
(c) 90
(d) 95.5
(e) None of the above
25. Refer to the previous problem. On the final exam Carla scored 93. What is the value of her residual?
(a) 98
(b) 2.5
(c) –2.5
(d) 0
(e) None of the above
26.) Suppose we fit the least squares regression line to a set of data. What do we call any individual points with
unusually large values of the residuals?
(a) Response variables
(b) The slope
(c) Outliers
(d) Correlations
(e) None of the above
27.) If removing an observation from a data set would have a marked change on the position of the LSRL fit to the
data, what is the point called:
(a) Robust
(b) A residual
(c) A response
(d) Influential
(e) None of the above
28.) What do we call a sample that consists of the entire population?
(a) A stratum
(b) A multistage sample
(c) A mistake. A sample can never be the entire population.
(d) A census
(e) None of the above. The answer is _________________________.
29.) In a population of students, the number of calculators owned is a random variable X with P(X = 0) = 0.2,
P(X=1) = 0.2, and P(X = 2) = 0.6. The mean of this probability distribution is
(a) 0
(b) 1.4
(c) 2.4
(d) 2.6
(e) The answer cannot be computed from the information given.
30.) Refer to the previous problem. The variance of this probability distribution is
(a) 0.36
(b) 0.63
(c) 0.64
(d) 0.46
(e) The answer cannot be computed from the information given.
31.) In a large population of college students, 20% of the students have experienced feelings of math anxiety. If
you take a random sample of 15 students from this population, the probability that exactly 2 students have
experienced math anxiety is
(a) 0.3020
(b) 0.2308
(c) 0.2013
(d) 0.5
(e) 1
(f) None of the above
32.) In a certain large population, 40% of households have a total annual income of $70,000. A simple random
sample of 8 of these households is selected. What is the probability that 3 or more of the households in the
survey have an annual income of over $70,000?
(a) 0.3456
(b) 0.4000
(c) 0.6846
(d) 0.5248
(e) The answer cannot be computed from the information given.
33.) To use a normal approximation to the binomial, which of the following does not have to be true?
a.
b.
c.
d.
e.
np ≥ 5, n(1 –p)≥ 5 (or: np ≥ 10, n (1–p) ≥10).
The individual trials must be independent.
The sample size in the problem must be too large to permit doing the problem on a calculator.
For the binomial, the population size must be at least 10 times as large as the sample size.
All of the above are true.
34.) Here are the IQ test scores of 10 randomly chosen fifth-grade students:
145
139
126
122
125
130
96
110
118
To make a stemplot of these scores, you would use as stems
A. 0 and 1.
B. 09, 10, 11, 12, 13, and 14.
C. 96, 110, 118, 122, 125, 126, 130, 139, and 145.
D. 0, 2, 3, 5, 6, 8, 9.
E. None of the above is a correct answer.
118
35.) Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to
study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this
study,
A. gas mileage is a response variable, and you expect to find a negative association.
B. gas mileage is a response variable, and you expect to find a positive association.
C. gas mileage is an explanatory variable, and you expect to find a strong negative association.
D. gas mileage is an explanatory variable, and you expect to find a strong positive association.
E. gas mileage is an explanatory variable, and you expect to find very little association.
36.) Which of the following is specifically related to the Population?
A. Statistic
B. Parameter
C. Subject
D. Response
E. Explanatory
37.) Which of the following is specifically related to the Sample?
A. Statistic
B. Parameter
C. Subject
D. Response
E. Explanatory
38 – 40 (Let’s set some goals)
Write down three things. Two things that you want me to work on (I will slow down when I talk sorry
that’s my Italian side I’ve been working on it). One thing you can do to get better.