Answer:
P(X = 2) = 0.3157
Step-by-step explanation:
Let assume that the question wants us to determine the probability that, let say when 5 customers are randomly selected, exactly 2 of the customers are comfortable.
Then;
p = 0.31
n = 5; x = 2
q = 1 - p
= 1 - 0.31
= 0.69
∴
The probability mass function is:
[tex]P(X =x) = ^n C_r * p^x *q^{n-x}[/tex]
[tex]P(X =x) = ^5 C_2 * (0.31)^2 *0.69^{5-2}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(5-2)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4*3!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4}{2!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) =10* (0.31)^2 *0.69^{3}[/tex]
P(X = 2) = 0.3157
