Movie trailers are designed to entice audiences by showing scenes from coming attractions. Several trailers are usually shown in a theatre before the start of the main feature, and most are available via the Internet. The duration of a movie trailer is approximately Normal, with mean 150 seconds and standard deviation 30 seconds.

(a) What is the probability that a randomly selected trailer lasts less than 2 minutes? (3 points)

(b) Any movie trailer that lasts beyond 4 minutes and 30 seconds is considered too long. What percentage of movie trailers is too long? (2 points)

(c) Ten percent of movie trailers have durations above what value? (3 points)

(d) In a sample of 16 randomly selected movie trailers, find the probability that the sample mean duration is greater than 3 minutes and 30 seconds. (3 points)