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5 February, 10:33

researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population prefers the color red. If 14 14 buyers are randomly selected, what is the probability that exactly 2 2 buyers would prefer red? Round your answer to four decimal places.

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  1. 5 February, 13:18
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    Answer: the probability that exactly 2 buyers would prefer red is 0.0320

    Step-by-step explanation:

    We would assume a binomial distribution for the color preferences of new car buyers. The formula is expressed as

    P (x = r) = nCr * p^r * q^ (n - r)

    Where

    x represent the number of successes.

    p represents the probability of success.

    q = (1 - r) represents the probability of failure.

    n represents the number of trials or sample.

    From the information given,

    p = 40% = 40/100 = 0.4

    q = 1 - p = 1 - 0.4

    q = 0.6

    n = 14

    x = r = 2

    Therefore,

    P (x = 2) = 14C2 * 0.4^2 * 0.6^ (14 - 2)

    P (x = 2) = 91 * 0.16 * 0.0022

    P (x = 2) = 0.0320
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