According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation o

Question

According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.07 inches. What is the probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days (taken over many years)?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

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Thu Hương 4 years 2021-09-03T05:18:07+00:00 1 Answers 19 views 0

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  1. Verity
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    2021-09-03T05:19:22+00:00
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    Answer:

    The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

    P(X≤ 0.11) = 0.4404

    Step-by-step explanation:

    Step(i):-

    Given that the mean of the Population = 0.10 inches

    Given that the standard deviation of the population = 0.07inches

    Let ‘X’ be a random variable in a normal distribution

    Z = \frac{x-mean}{S.D} = \frac{0.11-0.10}{0.07} = 0.1428

    Step(ii):-

    The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

    P(X≤ 0.11) = P(Z≤0.1428)

                   =  1-P(Z≥0.1428)

                  =  1 – ( 0.5 +A(0.1428)

                =  0.5 – A(0.1428)

                = 0.5 -0.0596

               = 0.4404

    Final answer:-

    The probability that the mean daily precipitation will be 0.11 inches or less for a random sample of November days

    P(X≤ 0.11) = 0.4404

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