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3 June, 01:40

The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the standard deviation of the sampling distribution of the sample mean x if a sample of 64 students is selected at random from the entire freshman class

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  1. 3 June, 03:37
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    Step-by-step explanation:

    We know that the mathematics test scores are normally distributed with mean μ=82 and standard deviation σ=8.

    We know that the central limit theorem states that a selected sample from a normal distribution with mean μ and standard deviation σ is also normally distributed with mean μxbar and standard deviation σxbar.

    Also, the sample mean of sampling distribution is μxbar=μ, where μ is population mean.

    The standard deviation of sampling distribution is σxbar=σ/√n where n is the sample size and σ is population standard deviation.

    The given sample size=n=64.

    So, the required standard deviation of sampling distribution is

    σxbar=σ/√n

    σxbar=8/√64

    σxbar=8/8

    σxbar=1.
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