A poll is given, showing 35% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly

Question

A poll is given, showing 35% are in favor of a new building project. If 8 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

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Sophia 2 months 2021-10-09T06:06:35+00:00 1 Answer 0 views 0

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    2021-10-09T06:07:58+00:00

    Answer:

    18.7%

    Step-by-step explanation:

     This is a case of binomial distribution. The formula is as follows:

    P = 8C4 * (p ^ x) * [(1-p) ^ (n-x)]

     

    Now, we have to p = 0.35, n = 8 and x = 4.

    8C4, means combinations of 8 in 4, the combination formula is:

    nCx = n! / [x! * (n-x)!]

    Replacing

    8C4 = 8! / [4! * (8-4)!] = 8! / (4! * 4!) = 70

    Now we can replace all values in the main formula:

    P = 70 * (0.35 ^ 4) * [(1-0.35)] ^ (8-4)

    P = 70 * (0.35 ^ 4) * (0.65 ^ 4) = 0.187

    Therefore, there is an 18.7% is the probability that exactly 4 of them favor the new building project

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45:7+7-4:2-5:5*4+35:2 =? ( )