Based on the data from Cumulative Review Exercise 7, assume that ages of moviegoers are normally distributed with a mean of 35 years and a standard deviation of 20 years.

a. What is the percentage of moviegoers who are younger than 30 years of age?
b. Find P25, which is the 25th percentile.
c. Find the probability that a simple random sample of 25 moviegoers has a mean age that is less than 30 years.
d. Find the probability that for a simple random sample of 25 moviegoers, each of the moviegoers is younger than 30 years of age. For a particular movie and showtime, why might it not be unusual to have 25 moviegoers all under the age of 30?

Listed below are annual high values of the Dow Jones Industrial Average (DJIA) and annual mean sunspot numbers for eight recent years. A sunspot number is a measure of sunspots or groups of sunspots on the surface of the sun. The DJIA is a commonly used index that is a weighted mean calculated from different stock values.

Data From Cumulative Review Exercise 7:

The table below shows the distribution of the ages of moviegoers (based on data from the Motion Picture Association of America). Use the data to estimate the mean, standard deviation, and variance of ages of moviegoers. Hint: For the open-ended category of “60 and older,” assume that the category is actually 60–80.