Question: A pest control company uses a certain pesticide as a perimeter barrier for residential customers. The pesticide has a mean effectiveness time of 37.8 days with a standard deviation of 7.8 days. Suppose that a random sample of 50 homes is chosen and the effectiveness time is measured for each application of the pesticide.

a) What is the distribution for the population we are sampling from?

b) What is the distribution for possible samples means?

c) Determine the probability that the sample mean obtained will be less than 40 days