Download Chapter 6 PRACTICE QUIZ – Random Variables (50 pts)

AP Statistics
Name:_________________________
Date:__________Period:_________
Chapter 6 PRACTICE QUIZ – Random Variables (50 pts)
Part 1: Multiple Choice. (3 points each)
_____1. In a population of homes, the number of phones owned is a random variable X with P(X=2) =
0.1, P(X=3) = 0.6 and P(X=4) = 0.3. The mean of this probability distribution is
a) 1
b) 3
c) 4
d) 3.2
e) The answer cannot be computed from the information given.
_____2. The number of calories in a one-ounce serving of a certain breakfast cereal is a random
variable with a mean 90 and standard deviation 2. The number of calories in a full cup of whole milk is
a random variable with mean 150 and standard deviation 3.5. For breakfast you eat one ounce of cereal
with ½ cup of whole milk. Let Z be the random variable that represents the total number of calories in
this breakfast. The mean of Z is
a) 150
b) 165
c) 195
d) 240
e) 120
_____3. Refer to the previous problem, question # 2. What is the standard deviation?
a) 5.5
b) 16.25
c) 4.03
d) 7.06
e) 2.66
_____4. Cans of soft drinks cost $1.25 in a certain vending machine. What is the expected value and
variance of daily revenue (Y) from the machine, if X, the number of cans sold per day, has E(X) = 200
and Var(X) = 48?
a) E(Y) = 250, Var(Y) = 50
b) E(Y) = 200, Var(Y) = 60
c) E(Y) = 200, Var(Y) = 75
d) E(Y) = 250, Var(Y) = 60
e) E(Y) = 250, Var(Y) = 75
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AP Statistics
_____5. A random variable X has a probability distribution as follows:
x
0 1 2
3
P(x) 2k 3k 13k 2k
Then the probability that P(X<2.0) is equal to
a) 0.15
b) 0.25
c) 0.5
d) 0.65
e) 0.75
_____6. A fifth-grade teacher gives homework every night in both mathematics and language arts. The
time to complete the mathematics homework has a mean of 30 minutes and a variance of 10 minutes.
The time to complete the language arts assignment has a mean of 40 minutes and a variance of 12
minutes. The time to complete the mathematics and the time to complete the language arts homework
have no correlation. The variance of the difference in time to complete both homework assignments
a) is less than 22 minutes since the no correlation tells you that more time on one assignment
will be associated with less time on the second assignment.
b) is 22 minutes because variance is always equal to the sum of the individual variances,
regardless of the correlation.
c) is greater than 22 minutes since we are subtracting squared standard deviations.
d) is 22 minutes, as would be the variance of the sum of times to complete both assignments.
e) is less than 22 minutes since we are adding squared standard deviations.
Mr. Page
page 2
AP Statistics
Name:___________________________
PART II - Answer completely, but be concise. Write sequentially and show all steps. Show all your
work. Indicate clearly the methods you used, because you will be graded on the correctness of your
methods as well as on the accuracy of your results and explanations.
7. A box contains ten $1 bills, five $2 bills, three $5 bills, one $10 bill, and one $1,000 bill. A person
charged $50 to select one bill at random.
a) Identify the random variable X =
(2 pt)
b) Construct a probability distribution for this data.
(3 pts)
c) Find the expected payout (this is not net of cost).
(3 pts)
d) Is the game fair? Explain briefly.
(3 pts)
8.
The density curve for a continuous random variable is shown below. Use this curve
to find the following probabilities:
a) P (x < 3 )
(3 pts)
0.5
b) P (1 < x < 2)
(3 pts)
c) P(x = 1)
(3 pts)
Mr. Page
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AP Statistics
9. For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. Let C
be the number of child tickets purchased by a single customer. The probability distribution of the
number of child tickets purchased by a single customer is given in the table below.
c
p(c)
0
1
2
3
0.2 0.4 0.3 0.1
a) Compute the mean and standard deviation of C.
(4 pts)
b) Suppose the mean and standard deviation for the number of adult tickets purchased by a single
customer are 1.4 and 0.6, respectively. Assume that the number of child tickets and adult tickets
purchased are independent random variables. Compute the mean and standard deviation of the
total number of adult and child tickets purchased by a single customer.
(4 pts)
c) Suppose each child ticket costs $10 and each adult ticket costs $15. Compute the mean and
standard deviation of the total amount spent per purchase.
(4 pts)
Mr. Page
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