Suppose that a random sample of 36 IQ scores is drawn from a population of IQ scores with mean = 100 and standard deviation = 15.
a. Find the standardized statistic for x‾ = 97.
b. Find the standardized statistic for x‾ = 105.
c. Give numerical values for the mean and standard deviation of the sampling distribution of x‾.
d. Draw a picture of the sampling distribution of x‾, and identify where x‾ = 97 and x‾ = 105 fall on the picture.
e. Draw a picture of the standard normal curve, and identify where the standardized statistics found in parts (a) and (b) fall on the picture.
f. What is the relationship between the pictures in parts (d) and (e)?