The incomes in a certain large population of college teachers have a normal dist

Question

The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $10,000. Four teachers are selected at random from this population to serve on a salary review committee. Do you know anything about the sampling distribution of the sample means coming from repeatedly taking samples of size 4 from the population of college teachers?

A) find the probability that an individual income from the population is greater than $90,000. In other words, find P(X > 90000). Explain.

B) find the probability that the mean of a sample of size 4 is greater than $90,000. In other words, find P(> 90000). Explain.

Explanation / Answer

If sample size = 4,

std error of sample = std dev/rt 4 = 5000

Mean = same 75000

A) P(X>90000) = P(Z>15000/10000) = 0.0668

B) P(x>90000) = P(Z>15000/5000) = P(Z>3) = 0.00000

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