A brand name has a 60 recognition rate Assume the owner of t

A brand name has a 60% 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 parts (a) through (d) below.

a. What is the probability that exactly 3 of the selected consumers recognize the brand name? (Round to three decimal places as needed.)

b. What is the probability that all of the selected consumers recognize the brand name? (Round to three decimal places as needed.)

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 3 an unusually high number of consumers that recognize the brand name?

A.No, because the probability that 3 or more of the selected consumers recognize the brand name is less than 0.05.

B. No, because the probability that 3 or more of the selected consumers recognize the brand name is greater than 0.05.

C.Yes, because the probability that 3 or more of the selected consumers recognize the brand name is less than 0.05.

D. Yes, because the probability that 3 or more of the selected consumers recognize the brand name is greater than 0.05.

Solution

probbility of recognising = 0.60

probability of not recognising = 0.40

a) P(3) = 4C3*(0.6)^3*(0.4)^1 = 0.3456

B)P(4) = 4C4*(0.6)^4*(0.4)^0 = 0.1296

C) ATLEAST 3 MEANS P(3)+P(4) = 0.3456+0.1296 =0.4752

D) AS WE HAVE CALCULATED THE PROBABILITY OF CHOOSING 3 OR MORE IS 0.4752

SO THE ANSWER WILL BE NO AS THE PROBABILITY IS GREATER THEN 0.05