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 3 4 5 6 7
frequency 4 7 38 22 7
3,4,5,6,7 (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 6.
{x = 6}
c. find p(x = 4)
p(x = 4)=0.090 (round to three decimal places as needed.)
d. obtain the probability distribution of x.

Explanation:

Step1: Calculate total frequency

Total frequency $=4 + 7+38 + 22+7=78$

Step2: Calculate probabilities for each value of X

For $X = 3$: $P(X = 3)=\frac{4}{78}\approx0.051$
For $X = 4$: $P(X = 4)=\frac{7}{78}\approx0.090$
For $X = 5$: $P(X = 5)=\frac{38}{78}\approx0.487$
For $X = 6$: $P(X = 6)=\frac{22}{78}\approx0.282$
For $X = 7$: $P(X = 7)=\frac{7}{78}\approx0.090$

Answer:

X	P(X)
4	0.090
5	0.487
6	0.282
7	0.090