Question

Based on a​ survey, assume that ​31% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly​ selected, exactly of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

Answer 1

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:

$P(X =x) = ^n C_r * p^x *q^{n-x}$

$P(X =x) = ^5 C_2 * (0.31)^2 *0.69^{5-2}$

$P(X =2) = \dfrac{5!}{2!(5-2)!} * (0.31)^2 *0.69^{3}$

$P(X =2) = \dfrac{5!}{2!(3)!} * (0.31)^2 *0.69^{3}$

$P(X =2) = \dfrac{5*4*3!}{2!(3)!} * (0.31)^2 *0.69^{3}$

$P(X =2) = \dfrac{5*4}{2!} * (0.31)^2 *0.69^{3}$

$P(X =2) =10* (0.31)^2 *0.69^{3}$

P(X = 2) = 0.3157