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)=0.093
(round to three decimal places as needed.)
d. obtain the probability distribution of x.
(round to three decimal places as needed.)
x p(x)
2
3
4
5
6

Explanation:

Step1: Calculate total frequency

Total frequency \( N=2 + 3+33 + 17+13=68\)

Step2: Calculate \(P(X = 2)\)

\(P(X = 2)=\frac{2}{68}\approx0.029\)

Step3: Calculate \(P(X = 3)\)

\(P(X = 3)=\frac{3}{68}\approx0.044\)

Step4: Calculate \(P(X = 4)\)

\(P(X = 4)=\frac{33}{68}\approx0.485\)

Step5: Calculate \(P(X = 5)\)

\(P(X = 5)=\frac{17}{68}=0.250\)

Step6: Calculate \(P(X = 6)\)

\(P(X = 6)=\frac{13}{68}\approx0.191\)

Answer:

\(X\)	\(P(X)\)
\(3\)	\(0.044\)
\(4\)	\(0.485\)
\(5\)	\(0.250\)
\(6\)	\(0.191\)