A city of punjab has 15 percemt chance of wet weather on any given day. What is probability that it will take a week for it three wet weathe

Question

A city of punjab has 15 percemt chance of wet weather on any given day. What is probability that it will take a week for it three wet weather on 3 sepaprate days? Also find it standard deviation

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Bơ 5 years 2021-08-11T08:30:49+00:00 1 Answers 23 views 0

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  1. dangkhoa
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    2021-08-11T08:32:19+00:00
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    Answer:

    The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447

    Explanation:

    We are given that A city of Punjab has 15 percent chance of wet weather on any given day.

    So, Probability of wet weather = 0.15

    Probability of not being a wet weather = 1-0.15 =0.85

    We are supposed to find probability that it will take a week for it three wet weather on 3 separate days

    Total number of days in a week = 7

    We will use binomial over here

    n = 7

    p =probability of failure = 0.15

    q = probability of success=0.85

    r=3

    Formula :P(r=3)=^nC_r p^r q ^{n-r}

    P(r=3)=^{7}C_{3} (0.15)^3 (0.85)^{7-3}\\P(r=3)=\frac{7!}{3!(7-3)!} (0.15)^3 (0.85)^{7-3}\\P(r=3)=0.06166

    Standard deviation =\sqrt{n \times p \times q}

    Standard deviation =\sqrt{7 \times 0.15 \times 0.85}

    Standard deviation =0.9447

    Hence The probability that it will take a week for it three wet weather on 3 separate days is 0.06166 and its standard deviation is 0.9447

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