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20 June, 12:03

Sixty dash fivesixty-five percent of households say they would feel secure if they had? $50,000 in savings. you randomly select 88 households and ask them if they would feel secure if they had? $50,000 in savings. find the probability that the number that say they would feel secure is? (a) exactly? five, (b) more than? five, and? (c) at most five.

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  1. 20 June, 12:24
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    To solve the following problems, we use the binomial probability equation:

    P (r) = [n! / (n-r) ! r!] p^r q^ (n-r)

    where,

    n = total number of households = 8

    r = number of sample

    p = probability of success = 65% = 0.65

    q = probability of failure = 0.35

    A. r = 5

    P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

    P (r=5) = 0.28

    B. r >5

    P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

    P (r=6) = 0.26

    P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

    P (r=7) = 0.14

    P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

    P (r=8) = 0.03

    Therefore total is:

    P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

    C. r ≤ 5

    P (r ≤ 5) = 1 - P (r>5)

    P (r ≤ 5) = 1 - 0.43

    P (r ≤ 5) = 0.57
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