Question

the following table displays a frequency distribution for the number of crew members on each shuttle mission over a 10 - year period. let x denote the crew size on a randomly selected shuttle from this time period.
crew size
frequency
2
5
3
7
4
33
5
17
6
13
...
a. what are the possible values of the random variable x?
2, 3, 4, 5, 6
(use a comma to separate answers as needed.)
b. use random - variable notation to represent the event that the shuttle mission obtained has a crew size of 5.
\\{x = 5\\}
c. find p(x = 3).
p(x = 3)=\square
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the total frequency

The total frequency is the sum of all frequencies: \(2 + 3+4 + 17+13\)

$$
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$$

Step2: Calculate \(P(X = 3)\)

The frequency for \(X = 3\) is \(7\). The probability \(P(X=3)\) is given by the formula \(P(X = k)=\frac{\text{Frequency of }k}{\text{Total frequency}}\)

$$P(X = 3)=\frac{7}{39}\approx0.179$$

Answer:

\(0.179\)