C. Verify that a standard normal distribution contains virtually all of the data in the interval m{3s? 6-53. the probability that a value from a normally distributed random variable will exceed the mean is 0.50. The same is true for the uniform distribution. Why is this not necessarily true for the exponential distribution? Discuss and show examples to illustrate your point. 6-79 The Future-Vision Digital and Satellite 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 come 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? C. Verify that a standard normal distribution contains virtually all of the data in the interval m{3s? 6-53. the probability that a value from a normally distributed random variable will exceed the mean is 0.50. The same is true for the uniform distribution. Why is this not necessarily true for the exponential distribution? Discuss and show examples to illustrate your point. 6-79 The Future-Vision Digital and Satellite 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 come 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