The random variable X is the crew size of a randomly selected shuttle mission. I
ID: 3059397 • Letter: T
Question
The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.
x
2
3
4
5
6
7
8
P(Xequals=x)
0.049
0.013
0.099
0.397
0.165
0.228
0.049
a.
Find and interpret the mean of the random variable.
mu=
(Round to three decimal places as needed.)
Interpret the mean. Choose the correct answer below.
A.
As the number of observations, n, decreases, the mean of the observations will approach the mean of the random variable.
B.
The observed value of the random variable will be less than the mean of the random variable in most observations.
C.
As the number of observations, n, increases, the mean of the observations will approach the mean of the random variable.
D.
The observed value of the random variable will be equal to the mean of the random variable in most observations.
b.
Obtain the standard deviation of the random variable.
sigmaequals=nothing
(Round to three decimal places as needed.)
c.
Draw a probability histogram for the random variable. Choose the correct graph below.
A.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.23; 3, 0.40; 4, 0.05; 5, 0.10; 6, 0.17; 7, 0.05; 8, 0.01.
Crew Size
234567800.10.20.30.40.5Probability
B.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.17; 3, 0.40; 4, 0.10; 5, 0.01; 6, 0.05; 7, 0.05; 8, 0.23.
Crew Size
234567800.10.20.30.40.5Probability
C.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.10; 3, 0.40; 4, 0.17; 5, 0.05; 6, 0.23; 7, 0.05; 8, 0.01.
Crew Size
234567800.10.20.30.40.5Probability
D.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.05; 3, 0.01; 4, 0.10; 5, 0.40; 6, 0.17; 7, 0.23; 8, 0.05.
Crew Size
234567800.10.20.30.40.5Probability
Click to select your answer(s).
x
2
3
4
5
6
7
8
P(Xequals=x)
0.049
0.013
0.099
0.397
0.165
0.228
0.049
Explanation / Answer
The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.
x
2
3
4
5
6
7
8
P(Xequals=x)
0.049
0.013
0.099
0.397
0.165
0.228
0.049
a.
Find and interpret the mean of the random variable.
mu=
(Round to three decimal places as needed.)
Interpret the mean. Choose the correct answer below.
A.
As the number of observations, n, decreases, the mean of the observations will approach the mean of the random variable.
B.
The observed value of the random variable will be less than the mean of the random variable in most observations.
C.
As the number of observations, n, increases, the mean of the observations will approach the mean of the random variable.
D.
The observed value of the random variable will be equal to the mean of the random variable in most observations.
b.
Obtain the standard deviation of the random variable.
sigmaequals=nothing
(Round to three decimal places as needed.)
c.
Draw a probability histogram for the random variable. Choose the correct graph below.
A.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.23; 3, 0.40; 4, 0.05; 5, 0.10; 6, 0.17; 7, 0.05; 8, 0.01.
Crew Size
234567800.10.20.30.40.5Probability
B.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.17; 3, 0.40; 4, 0.10; 5, 0.01; 6, 0.05; 7, 0.05; 8, 0.23.
Crew Size
234567800.10.20.30.40.5Probability
C.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.10; 3, 0.40; 4, 0.17; 5, 0.05; 6, 0.23; 7, 0.05; 8, 0.01.
Crew Size
234567800.10.20.30.40.5Probability
D.
A histogram titled Crew Size has a horizontal axis labeled from 2 to 8 in increments of 1 and a vertical axis labeled Probability from 0 to 0.5 in increments of 0.1. The histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis labels. The approximate heights of the vertical bars are as follows, where the horizontal axis value is listed first and the height is listed second: 2, 0.05; 3, 0.01; 4, 0.10; 5, 0.40; 6, 0.17; 7, 0.23; 8, 0.05.
Crew Size
234567800.10.20.30.40.5Probability
Click to select your answer(s).
x
2
3
4
5
6
7
8
P(Xequals=x)
0.049
0.013
0.099
0.397
0.165
0.228
0.049