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AP Statistics
Chapter 7 – Take Home Assignment
Mean and Variance of Random Variables Practice
Name __________________________
1. Determine whether the distribution represents a probability distribution. If it does not, state why.
a)
X
3
6
8
12
P(X)
0.3
0.5
0.7
-0.8
b)
X
2
5
6
8
10
P(X)
2/11
3/11
3/11
2/11
1/11
c)
X
20
30
40
50
P(X)
0.05
0.35
0.4
0.3
2. Construct a probability distribution for the data and draw a graph for the distribution. The probabilities that a
student volunteer hosts 1, 2, 3, or 4 prospective first-year students are 0.4, 0.3, 0.2, and 0.1 respectively.
3. State whether the variable is discrete or continuous.
a) the speed of a jet airplane
b) The number of cheeseburgers a fast-food restaurant serves each day
c) The number of people who play the state lottery each day
AP Statistics
4. Construct a probability distribution for drawing a card from a deck of 40 cards consisting of 10 cards
numbered 1, 10 cards numbered 2, 15 cards numbered 3,
and 5 cards numbered 4.
X
a) P(X< 4) =
d) P(X > 2) =
P(X)
b) P(X<2) =
e) P(X = 3) =
c) P(2 < X < 4) =
5. A density curve is pictured below. Use the distribution
to find the following probabilities.
a) P(X < 1) =
b) P(X > 2) =
c) P(X = 3) =
d) P(1 < X < 3) =
1
2 3
4
5
6
6. Each month, an American household generates an average of 28 pound of newspaper for garbage or
recycling. Assume the variable is approximately normally distributed and the standard deviation is 2 pounds.
If a household is selected at random, find the probability of its generating
a) More than 30.2 pounds per month
b) Between 27 and 31 pounds per month
7. For a medical study, a researcher wishes to select people in the middle 60% of the population based on
blood pressure. The blood pressure readings are normally distributed. If the mean systolic blood pressure is
120 and the standard deviation is 8, find the upper and lower reading that would qualify people to participate in
the study.
AP Statistics
8. The probabilities that a randomly selected customer purchases 1, 2, 3, 4, or 5 items at a convenience store
are 0.32, 0.12, 0.23, 0.18, and 0.15, respectively.
(a) Construct a probability distribution (table) for the data, and verify that this is a legitimate probability
distribution.
(b) Calculate µx. Interpret this value in the context of this problem.
(c) Find the standard deviation of X.
(d) Suppose two customers, A and B, are selected at random. Find the mean and standard deviation of
the difference in the number of items purchased by A and by B. Show your work.
9. Suppose that the mean height of policemen is 70 inches with a standard deviation of 3 inches. And suppose
that the mean height for policewomen is 65 inches with a standard deviation of 2.5 inches.
If heights of policemen and policewomen are Normally distributed, find the probability that a randomly
selected policewoman is taller than a randomly selected policeman.
10. A single toss of a balanced coin has either 0 or 1 head, each with probability 1/2. What are the mean and
standard deviation of the number of heads?
AP Statistics
11. Toss a coin four times. Use the rules for means and variances to find the mean and standard deviation of
the total number of heads.
12. Scores on the Mathematics part of the SAT college entrance exam in a recent year had mean 519 and
standard deviation 115. Scores on the Verbal part of the SAT had mean 507 and standard deviation 111.
(a) What is the mean of the total SAT score (Math plus Verbal)?
(b) If you can calculate the standard deviation of the total SAT score, do it. If not, explain clearly why you
can’t.