In the normal distribution with any given mean and standard deviation, we know that approximately

68% of the observations fall within one standard deviation of the mean

95% of the observations fall within two standard deviations of the mean

99.7% of the observations fall within 3 standard deviations of the mean.

This is sometimes called the 68-95-99.7Empirical Rule-of-Thumb.

Using the 68-95-99.7Empirical Rule-of-Thumb, answer the following questions. No partial credit will be given for using any other method.

a.If a population has mean 100 and standard deviation 20, what is the mean of the sampling distribution of sample size n = 25?

b.If a population has mean 100 and standard deviation 20, what is the standard deviation of the sampling distribution of sample size n = 25?

c.A given exam has a normal distribution with a mean of 70 and a standard deviation of 10.A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to fall between 66 and 74?%

d.A given exam has a normal distribution with a mean of 70 and a standard deviation of 10.A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be less than 70?%

e.A given exam has a normal distribution with a mean of 70 and a standard deviation of 10.A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be greater than 68?%