Consider a population with a mean=187 and standard deviation=84. Suppose random samples of sizen=87

are selected from this population.

1. a) What is the mean of the distribution of the sample mean?

x= ............

b) What is the standard error of the mean? (2 decimal places)

x= .........

In the following questions, round the standard error andz-scoresto exactly2 decimal placesbefore determining probabilities. Report probabilities accurate to at least 3 decimal places.

1. What is the probability that a randomly selected sample mean is:

a) greater than 172.6?

b) less than 184.6?

c) greater than 172.6 and less than 184.6?

d) greater than 172.6 given less than 184.6?

e) greater than 172.6 or greater than 184.6?

Between what values would you expect to find the middle 66% of the sample means?

Round to the nearest integer.

Place the smaller value in the first box and the larger value in the second box.

1. Between...........and.........

1. Why are we able to use the normal distribution in the calculations above?

• Becasuse the standard error is large enough
• Because the sample size is large enough
• Because the original population is normal
• Because the sample mean is large enough