Question 1 - Given the probability function R(x) = 0.2 for x = 0, 1, 2, 3, 4, find the mean and standard deviation.
Question 2 - The number of children living per household, x, in the United States in 2008 is expressed as a probability distribution here.
|
x
|
0
|
1
|
2
|
3
|
4
|
5+
|
|
P(x)
|
0.209
|
0.384
|
0.249
|
0.106
|
0.032
|
0.020
|
SOURCE: U.S. Census Bureau
a. Is this a discrete probability distribution? Explain.
b. Draw a histogram for the distribution of x, the number of children per household.
c. Replacing "5+" with exactly "5," find the mean and standard deviation.
Question 3 - Is a dog man's best friend? One would think so with 60 million pet dogs nationwide. But how many friends are needed? In the American Pet Products Association's 2007-2008 National Pet Owners Survey, the following statistics were reported.
|
Number of Pet Dogs
|
Percentage
|
|
One
|
63
|
|
Two
|
25
|
|
Three or more
|
12
|
SOURCE: APPA 2007-2008 National Pet Owners Survey
a. Is this a discrete probability distribution? Explain.
b. Draw a relative frequency histogram to depict the results shown in the table.
c. Replacing the category "three or more" with exactly "three," find the mean and standard deviation of the number of pet dogs per household.
d. How do you interpret the mean?
e. Explain the effect that replacing the category "three or more" with "three" had on the mean and standard deviation.
Question 4 - As reported at the beginning of the chapter, Americans are in love with the automobile - the majority have more than one vehicle per household. In fact, the national average is 2.28 vehicles per household. The number of vehicles per household in the United States can be described as follows:
|
Vehicles, x
|
P(x)
|
|
1
|
0.34
|
|
2
|
0.31
|
|
3
|
0.22
|
|
4
|
0.06
|
|
5
|
0.03
|
|
6
|
0.02
|
|
7
|
0.01
|
|
8 or more
|
0.01
|
a. Replacing the category "8 or more" with exactly "8," find the mean and standard deviation of the number of vehicles per household in the United States.
b. How does the mean calculated in part (a) correspond to the national average of 2.28?
c. Explain the effect that replacing the category "8 or more" with "8" had on the mean and standard deviation.
Question 5 - The random variable A has the following probability distribution:
|
A
|
1
|
2
|
3
|
4
|
5
|
|
P(A)
|
0.6
|
0.1
|
0.1
|
0.1
|
0.1
|
a. Find the mean and standard deviation of A.
b. How much of the probability distribution is within 2 standard deviations of the mean?
c. What is the probability that A is between μ - 2σ and μ + 2σ?