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:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...[/tex]
Compute the value of P (X = 3) as follows:
[tex]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[/tex]
Thus, the probability that exactly three of them are comfortable with delivery by drones is 0.2583.
