Question

A brand name has 20% recognition rate.

5) A brand name as a 20% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 4 randomly selected consumers. Complete part (a) through (d) below. Answer the following questions using the appropriate formula (Round to three decimal places). a. Find the probability that exactly 3 of the 4 consumers recognize the brand name. b. What is the probability that all of the selected consumers recognize the brand name? c. What is the probability that at least 3 of the selected consumers recognize the brand name? d. If 4 consumers are randomly selected, is at least 3 an unusual high number of consumers that recognize the brand name?

Answer 1

X ~ B(4, 0.20)

Hence,

a) P(X = 3)

$= \binom{4}{3} (0.20)^3(0.80)^{4-3}$

= 0.0256

b) P(All 4) = (0.20)⁴ = 0.0016

c) P(Atleast 3) = P(3) + P(4) = 0.0256 + 0.0016 = 0.0272

d) Yes, atleast 3 is unusually high number because its probability is less than 0.05.