1) A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $850,000,

and the standard deviation is $200,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year is recorded

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

b. What is the probability that the sample mean exceeds $855,000?

c. What is the probability that the sample mean exceeds $839,000?

d. What is the probability that the sample mean is between $836,000 and $863,000?

2) A random sample of 100 voters is taken to estimate the proportion of a state's electorate in favor of increasing the gasoline tax to provide additional revenue for highway repairs. Suppose that it is decided that a sample of 100 voters is too small to provide a sufficiently reliable estimate of the population proportion. It is required instead that the probability that the sample proportion differs from the population proportion (whatever its value) by more than 0.06 should not exceed 0.05.

How large a sample is needed to guarantee that this requirement is met?

a) The sample size n needs to be at least ______.

(Round up to the nearest whole number.)

3) An employee survey conducted by a company two years ago found that 53% of its employees were concerned about future health care benefits. A random sample of 75 of these employees were asked if they were now concerned about future health care benefits. Answer the following, assuming that there has been no change in the level of concern about health care benefits compared to the survey two years ago.

a. What is the standard error of the sample proportion who are concerned?

b. What is the probability that the sample proportion is less than 0.50?

c. What is the upper limit of the sample proportion such that only 4% of the time the sample proportion would exceed this value?