In a certain country, the average age is 31 years old and the standard deviation is 4 years. If we select a simple random sample of 100 peop

Question

In a certain country, the average age is 31 years old and the standard deviation is 4 years. If we select a simple random sample of 100 people from this country, what is the probability that the average age of our sample is at least 32?

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Ayla 2 weeks 2021-09-10T14:16:30+00:00 1 Answer 0

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    2021-09-10T14:18:24+00:00

    Answer: 0.0062

    Step-by-step explanation:

    Given : Mean : \mu=\ 31

    Standard deviation :\sigma= 4

    Sample size : n=100

    Assume that age of people in the country is normally distributed.

    The formula to calculate the z-score :-

    z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

    For x = 32

    z=\dfrac{32-31}{\dfrac{4}{\sqrt{100}}}=5

    The p-value = P(x\geq32)=P(z\geq5)

    =1-P(z<5)=1- 0.9937903\approx0.0062

    Hence, the the probability that the average age of our sample is at least =0.0062

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