Question

Based on a survey, assume that 26% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.

Answer 1

26% of consumers are comfortable having drones deliver their purchases.

Thus p = 0.26    { probability of success }

And q = 1 - p = 1-0.26 = 0.74

To find the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones.

So here we need to find P(X=3)

Thus here n = 5             { number of random samples/consumers selected }

And here x = 3              {i.e to find exactly three consumers comfortable with delivery by drones }

Thus

n = 5

x = 3

p = 0.26

q = 0.74

Here X ~ B( n = 5 , p = 0.26 )

i.e X follows binomial distribution with probability of success p = 0.26.

Now pmf is given by

P(X=x)   = nCx px q (n-x)

Here we need to find P(X=3)

P(X=3) =  5C3 p3 q (5-3)

P(X=3) = 5C3 * (0.26)3 * (0.74) (5-3)

P(X=3) = 10 * 0.017576 * 0.5476

P(X=3) = 0.09624618

P(X=3) = 0.09625

Thus , the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones is equal to 0.09625 .