The question is: 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 by each member is 15 minutes with standard deviation 2 minutes. Consider a random sample of 35 members who use a tanning booth.

(a) What is the approximate distribution of the sample average time spent tanning for the sample of 35 members?

(b) Find the probability that the total time spent tanning by the 35 members of the sample is between 8 and 9 hours.

(c) If the total time spent on a day when 35 members tan 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?

We may use the central distribution theory to answer that question, but I'm unsure if this is the right way to answer the question.