The variance of the scores on a skill evaluation test is 143,641 with a mean of 1517 points. If 343 tests are sampled, what is the probabil

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The variance of the scores on a skill evaluation test is 143,641 with a mean of 1517 points. If 343 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 36 points

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Thu Nguyệt 5 years 2021-08-11T17:14:54+00:00 1 Answers 18 views 0

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  1. binhan
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    2021-08-11T17:16:05+00:00
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    Answer:

    The probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

    Step-by-step explanation:

    We are given that

    The variance of the scores on a skill evaluation test=143,641

    Mean=1517 points

    n=343

    We have to find the probability that the mean of the sample would differ from the population mean by less than 36 points.

    Standard deviation,\sigma=\sqrt{143641}

    P(|x-\mu|<36)=P(|\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}|<\frac{36}{\frac{\sqrt{143641}}{\sqrt{343}}})

    =P(|Z|<\frac{36}{\sqrt{\frac{143641}{343}}})

    =P(|Z|<1.76)

    =0.9216

    Hence,  the probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

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