Question

Space Shuttles. The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 12, 1981 to July 8, 2011.

Crew Size	2	4	5	6	7	8
Frequency	4	3	36	28	63	1

Let X denote the crew size of a randomly selected shuttle mission between the aforementioned dates.

a. What are the possible values of the random variable X?

b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7.

c. Find P(X = 4); interpret in terms of percentages.

d. Obtain the probability distribution of X.

e. Construct a probability histogram for X.

Short answer

Part a.

The possible values for X: {2,4,5,6,7,8}

Part b.

X = 7

Part c.

P(X = 4) = 4/135

Part d.

Random Variable	Probability
2	4/135
4	3/135
5	36/135
6	28/135
7	63/135
8	1/135

Part e.

Step-by-step solution

Part (a) Step 1. Given information

From April 12, 1981, through July 8, 2011, the following table shows the frequency distribution of the number of crew members on each shuttle mission:

Crew Size	2	4	5	6	7	8
Frequency	4	3	36	28	63	1

Let's say the crew size of a shuttle trip that took place between the aforementioned dates.

Part (a) Step 2. Calculation

The number of crew members on the shuttle mission can be 2, 4, 5, 6, 7 or 8 according to the frequency distribution table. As a result, the following are feasible X values:

X = {2,4,5,6,7,8}

Part (b) Step 1. Solution 

If the shuttle mission includes a crew of size 7, it can be stated as follows:

X = 7

Part (c) Step 1. Solution 

By f/N rule:

P(X = 4) = 4/135

Part (d) Step 1. Solution

Random Variable	Probability
2	4/135
4	3/135
5	36/135
6	28/135
7	63/135
8	1/135

Part (e) Step 1. Solution 

The probability histogram for the random variable X is as follows: