What is the probability that exactly 3 of the selected consumers recognize the b

Question

What is the probability that exactly 3 of the selected consumers recognize the brand name? The probability that exactly 3 of the 4 consumers recognize the brand name is What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is What is the probability that at least 3 of the selected consumers recognize the br4and name? The probability that at least 3 of the selected consumers recognize the brand name is If 4 consumers are randomly selected, is 3 an unusually high number of consumers that recognize the brand name? No, because the probability that 3 or more of the selected consumers recognize the brand name is greater than 0.05 No, because the probability that 3 or more of the selected consumers recognize the brand name is less than 0.05.

Explanation / Answer

Let X be the random variable that number of consumers recognize the brand name.

Here X ~ Binomial(n=4, p=40%=0.4)

X has probability mass function is,

P(X=x) = (4 C x) * 0.4x * (1-0.4)4-x

P(X=3) = 0.154

The answer for the part a) is correct.

b) Here we have to find P(X=4).

P(X=4) = (4 C 4) * 0.44 * (1-0.4)4-4

= 0.0256

c) In this part we have to find P(X 3) = P(X=3) + P(X=4) = 0.154 + 0.0256 = 0.179

d) In this part we have to say that P(X=3) is unusually high or unusually low.

P(X=3) = 0.154

If P(x or more) < 0.05 then we say that it is unusually high otherwise unusually low.

But here probability is > 0.05

Therefore it is unusually low.

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