Recent research studies suggest that lycopene, found in tomatoes, may reduce the risk of certain cancers. According to the USDA/NCC Carotenoid Database for U.S. Foods, the mean amount of lycopene in a...

Recent research studies suggest that lycopene, found in tomatoes, may reduce the risk of certain cancers. According to the USDA/NCC Carotenoid Database for U.S. Foods, the mean amount of lycopene in a medium-sized fresh tomato is 3.7 milligrams (mg). Suppose the amount of lycopene is a normal random variable with standard deviation 1 mg. Consider the sample mean based on 5 observations

A health club recently added tanning booths in addition to a weight room, pool, and racquetball courts. For insurance purposes, an employee maintains careful records of the length of time each member spends in a tanning booth. The mean length of time spent tanning is 15 minutes with standard deviation 2 minutes. Consider a random sample of 35 members who use a tanning booth.

a. Find the distribution of the total time spent tanning by the 35 members, T.

b. Find the probability that the total time spent tanning is between 8 and 9 hours.

c. If the total time spent tanning is more than 9.2 hours, an employee must work overtime. What is the probability that the employee works overtime on a day when 35 members tan?

d. Find a value t such that P