A large number of people responded to a Community Tracking Study survey question that asked them to rate their satisfaction with their health plan, on a scale of 0 to 10.
a. Tell whether the distribution is left-skewed, right-skewed, or fairly symmetric.
b. What is the probability of a rating greater than 9?
c. It can be shown that the ratings have mean 7.6 and standard deviation 1.9. What would be the mean and standard deviation of the distribution of sample mean rating, for random samples of size 100?
d. What is the z-score for a mean rating of 9 in a sample of size 100?
e. Characterize a mean rating greater than 9 in a random sample of size 100 taken from this distribution as being not improbable, somewhat improbable, very improbable, or virtually impossible.
f. Explain why the methods of this chapter cannot be used to find the probability of a mean rating greater than 9 in a sample of size 10, instead of 100.