Question: a). The number of viewers ordering a particular pay-per-view program is normally distributed. 20% of the time, fewer than 20,000 people order the program. Only 10% of the time more than 28,000 people order the program. What is the mean and standard deviation of the number of people ordering the program?

b). It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread. If, over the course of a month, a household receives 150 pieces of unsolicited mail, what is the probability that the household discards more than 80 pieces of the mail without reading it? Use the normal approximation to the binomial distribution without the continuity correction?

c). The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 minutes and a standard deviation of 1.3 minutes. If the sandwich shop employees make $6.00 an hour, what is the mean and standard deviation for the labor costs per sandwich?

d). you are the owner of a small casino in Las Vegas. You want to reward the high rollers who come to your casino. You want to give free accommodations to no more than 10% of your patrons. Suppose that the mean amount wagered by all patrons is $287, with a standard deviation of $15. What is the minimum amount patron must wager to enjoy free accommodation?