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6 December, 00:50

In a survey, 70% of Americans said they own an answering machine. If 5 Americans are selected at random:

a. Find the probability that exactly 3 own an answering machine;

b. Find the mean number of people who own an answering machine.;

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Answers (2)
  1. 6 December, 01:07
    0
    B. find the mean number of people who own one
  2. 6 December, 01:19
    0
    Step-by-step explanation:

    We would assume a binomial distribution for the Americans that own answering machines. 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 = 70% = 70/100 = 0.7

    q = 1 - p = 1 - 0.7

    q = 0.3

    n = 5

    x = r = 3

    Therefore,

    P (x = 3) = 5C3 * 0.7^3 * 0.3^ (5 - 3)

    P (x = 3) = 10 * 0.343 * 0.09

    P (x = 3) = 0.3087

    b) mean = np = 5 * 0.7 = 3.5
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