WorksheetsAP Statistics Random Variables
Total questions: 20
Worksheet time: 1hrs 4mins
Name
Class
Date
1.
Which of the following is not a random variable?
a)
The heights of randomly-selected buildings in New York City.
b)
The suit of a card randomly-selected from a 52-card deck.
c)
The number of children in randomly-selected households in the United States.
d)
The amount of money won (or lost) by the next person to walk out of a casino in Las Vegas.
2.
A random variable is
a)
a hypothetical list of the possible outcomes of a random phenomenon.
b)
any phenomenon in which outcomes are equally likely.
c)
any number that changes in a predictable way in the long run.
d)
a variable whose value is a numerical outcome associated with a random phenomenon.
3.
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win.
Which of the following is the expected value of X?
Which of the following is the expected value of X?
a)
$1.00
b)
$2.50
c)
$4.00
d)
$6.00
4.
A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.
The mean number of customers that make a purchase during the first hour that the store is open is:
The mean number of customers that make a purchase during the first hour that the store is open is:
a)
2.0
b)
2.5
c)
2.9
d)
3
5.
A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is
a)
0.2
b)
1.4
c)
2.0
d)
3.0
6.
The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is
a)
.1056
b)
.3944
c)
.1042
d)
.8944
7.
Which of the following random variables is NOT continuous?
a)
Amount of gasoline in a car.
b)
Time it takes to commute to work.
c)
Number of goals scored by a hockey team.
d)
Lifetime of a AAA battery.
8.
Cool TV game show
Players win prizes with probabilities shown:
P($0) = .70
P($500) = .25
P($5,000) = .05
What are the mean and the standard deviation of the prize variable?
Players win prizes with probabilities shown:
P($0) = .70
P($500) = .25
P($5,000) = .05
What are the mean and the standard deviation of the prize variable?
a)
Mu = $375; sigma = $361
b)
Mu = $375; sigma = $1,083
c)
Mu = $1,833; sigma = $1,816
d)
Inadequate info is provided.
9.
A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the st. dev of X - Y?
a)
0.52
b)
0.72
c)
1.0
d)
Not here
10.
A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the mean of X + Y?
a)
13
b)
6.5
c)
14
d)
Not here.
11.
If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall?
a)
-5
b)
-2
c)
2
d)
5
12.
Suppose that a normal model describes the acidity (pH) of rainwater, and that water tested after last week’s storm had a z-score of 1.8. This means that the acidity of the rain
a)
had a pH 1.8 higher than average rainfall.
b)
had a pH of 1.8.
c)
varied with standard deviation 1.8
d)
had a pH 1.8 standard deviations higher than that of average rainwater.
13.
Find the value for
P(Z > 2.46)
P(Z > 2.46)
a)
0.00714
b)
0.99305
c)
0.00695
d)
0.99286
14.
Find the z-score such that 30% of the standard normal curve lies to the left of z.
a)
-1.88
b)
0.52
c)
-0.52
d)
1.88
15.
A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution:
X 0 1 2 3 4 5
P(X) 0.24 0.37 0.20 0.11 0.05 0.03
What is the probability that a randomly chosen household has at least two cars?
X 0 1 2 3 4 5
P(X) 0.24 0.37 0.20 0.11 0.05 0.03
What is the probability that a randomly chosen household has at least two cars?
a)
0.20
b)
0.29
c)
0.39
d)
0.61
16.
Random variable X is normally distributed with mean 10 and standard deviation 3, and random variable Y is normally distributed with mean 9 and standard deviation 4. If X and Y are independent, which of the following describes the distribution of Y - X?
a)
Normal with mean 1 and standard deviation -1
b)
Normal with mean -1 and standard deviation -1
c)
Normal with mean -1 and standard deviation 5
d)
Normal with mean -1 and standard deviation 7
17.
Suppose that a detailed study has revealed that for romance novels the number of pages has mean 364 and standard deviation of 47, and that for detective novels the number of pages has mean 404 and standard deviation 173. A reader is going to select at random one romance novel, independently selected at random one detective novel and read both book. What is the expected number of total pages the person will read?
a)
988
b)
768
c)
543.8
d)
40
18.
Suppose that a detailed study has revealed that for romance novels the
number of pages has mean 364 and standard deviation of 47, and that for
detective novels the number of pages has mean 404 and standard deviation
173. A reader is going to select at random one romance novel,
independently selected at random one detective novel and read both
book. What is the standard deviation of the total number of pages the person will read?
a)
14.8
b)
110.0
c)
179.3
d)
220.0
19.
In a large country, the distribution of the heights of married men is normal with mean 68.9 inches and standard deviation 2.9 inches. The distribution of the heights of married women is normal with mean 63.8 and standard deviation 2.5 inches.
A married couple is to be chosen at random. Let the random variable Z be the sum of the height of the man and the height of the woman.
Which of the following statements can be concluded from the information given?
I. Mean of Z = 68.9 + 63.8
II. Standard Deviation of Z = sqrt(2.92 + 2.52)
III. The distribution of Z is normal.
a)
I only
b)
III only
c)
I and II only
d)
I, II and III
20.
Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. What is the expected amount you win?
a)
$0.00
b)
-$1.00
c)
$1.00
d)
$3.00
100 %
