A town has 500 real estate agents. The mean value of the properties sold in a ye

Question

A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000 and the standard deviation is $300,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year is recoreded.

a. What is the standard error of the sample mean?

b. What is the probability that the sample mean exceeds $ 825,000?

c. What is the probability that the sample mean exceeds $ 780,000?

d. What is the probability that the sample mean is between 790,000 and 820,000?

Explanation / Answer

Given mean=800000, s=300000, n=100 a. the standard error of the sample mean = s/vn =300000/10 =30000 b. P(xbar>825000)= P((xbar-mean)/(s/vn) > (825000-800000)/30000) =P(Z>0.83) = 0.2033 (check standard normal table) c. P(xbar>780000) = P(Z>(780000-800000)/30000) =P(Z>-0.67) = 0.7486 (check standard normal table) d. P(790000

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