The Future-Vision Cable TV Company recently surveyed its customers. A total of 548 responses were received. Among other things, the respondents were asked to indicate their household income. The data from the survey are found in a file named Future-Vision.
a. Develop a frequency histogram for the income variable. Does it appear from the graph that income is approximately normally distributed? Discuss.
b. Compute the mean and standard deviation for the income variable.
c. Referring to parts a and b and assuming that income is normally distributed and the sample mean and standard deviation are good substitutes for the population values, what is the probability that a Future-Vision customer will have an income exceeding $40,000?
d. Suppose that Future-Vision managers are thinking about offering a monthly discount to customers who have a household income below a certain level. If the management wants to grant discounts to no more than 7% of the customers, what income level should be used for the cutoff?