Question

Sixty-five percent of consumers prefer to purchase electronics online. You randomly select consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five. (a) Find the probability that the number that prefer to purchase electronics online is exactly five. P(5)= (Round to three decimal places as needed.) (b) Find the probability that the number that prefer to purchase electronics online is more than five POX >5) NRound to three decimal places as needed.) (c) Find the probability that the number that prefer to purchase electronics online is at most five POX 55) = (Round to three decimal places as needed.)

Answer 1

Let X denotes the number of consumers who prefer to purchase electronics online out of 8 randomly selected consumers.

X ~ Binomial(n = 8, p = 0.65)

The probability mass function of X is

P(X = z) = * 0.65"* (1 - 0.65)8-1, 1 = 0, 1, 2, ..., 8

a)

P(X = 5) = * 0.655 * (1 – 0.65)8-5 = 0.278586 – 0.279

b)

P(X > 5) = 1 - P(X < 5) = 1 – *0.65** (1 - 0.65)8-1 = 1/ 1 – 0.572186 = 0.427814 0.428

c)

P(X <5) = * 0.65** (1 -0.65) 8-1 = 0.572186 0.572 T=0