1. For earthquakes with a magnitude 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 498 days and a standard deviation of 357 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of 7.5 or greater on the Richter scale.

a. On average, what would you expect to be the mean of the four times?

b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.)

2. A variable of a population has a mean of =74 and a standard deviation of =18.

a. Identify the sampling distribution of the sample mean for samples of size 81.

b. In answering part (a), what assumptions did you make about the distribution of the variable?

c. Can you answer part (a) if the sample size is 16instead of81? Why or why not?

3. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is

$1150, determine the probability that the mean tariff rate of 250randomly selected railroad-car shipments of ethanol will be within$100 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

What the probability is?

enter your response here.

There is about a % chance that the sampling error made in estimating the tariff rate of all railroad-car shipments of ethanol will be (Round to one decimal place as needed.) variance of the mean