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3. Suppose college faculty members with the rank of professor at two-year institutions earn an average of $52,500 per year with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all two-year institutions in the United States. A. What are the mean and standard deviation of the sampling distribution for n

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Answer:

The right answer is "516.3978".

Step-by-step explanation:

Given:

Sample mean,

[tex]\mu=52500[/tex]

Standard deviation,

[tex]\sigma=4000[/tex]

Random sample,

[tex]n = 60[/tex]

We can say that, the sample mean will be equivalent to the population mean.

So,

⇒  [tex]\mu_\bar x=\mu[/tex]

        [tex]=52500[/tex]

hence,

The standard deviation will be:

⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

        [tex]=\frac{4000}{\sqrt{60} }[/tex]

        [tex]=516.3978[/tex]

 

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