Question: Cereal A company's cereal boxes advertise 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounces.
(a) What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal? Show your work.
(b) Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal x - in these boxes is 9.65 ounces or less? Show your work.