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

1

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.