Suppose that college faculty 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 instituations in the united states

C) calculate the probability the sample mean x-bar is greater than $55,000.

D) If you drew a random sample with the mean $55,000 would you consider this sample unusual? What conclusions might you draw?

Question

Mathematics

Trevor Spencer

22 February, 11:10

Suppose that college faculty 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 instituations in the united states

C) calculate the probability the sample mean x-bar is greater than $55,000.

D) If you drew a random sample with the mean $55,000 would you consider this sample unusual? What conclusions might you draw?

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Answers (1)

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Triston Monroe · Answer 1

Let x be a random variable representing the mean saraly of professors at two year institutions, then

P (x > 55000) = 1 - P (z < (55000 - 52500) / 4000) = 1 - P (z < 0.625) = 1 - 0.73401 = 0.26599