Question

Based on a​ survey, assume that 43​% 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

Answer:

The probability that exactly three of them are comfortable with delivery by drones is 0.2583.

Step-by-step explanation:

Let X = number of consumers comfortable having drones deliver their purchases.

The probability of the random variable X is, P (X) = p = 0.43.

Then q is, q = 1 - p

A sample of n = 5 consumers are selected.

The random variable X follows a Binomial distribution with parameters n and p.

The pmf of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

Compute the value of P (X = 3) as follows:

$P(X=3)={5\choose 3}0.43^{3}(1-0.43)^{5-3}\\=10\times 0.079507\times 0.3249\\=0.258318\\\approx0.2583$

Thus, the probability that exactly three of them are comfortable with delivery by drones is 0.2583.