The general manager of a cosmetics marketing company believes the annual incomes of its clients are normally distributed. The following data represent the distribution of incomes for a random sample of the company’s clients. Given a sample mean of $67 000 and a standard deviation of $24 000, use the chi-square goodness-of-fit test to determine whether this distribution is significantly different from the normal distribution. Assume that ???? =0.05. How could the result help the company to sell more cosmetics?

Annual income of client ($) ......................... Frequency
0–20 000 ............................................................... 2
20 001–50 000 .................................................... 20
50 001–80 000 .................................................... 51
80 001–110 000 .................................................. 22
110 001–140 000 .................................................. 5