This Christmas, you have a seasonal job in a bookstore. \(T\), the number of minutes until the next customer asks about the book Home Engineering is exponentially distributed with parameter \(\lambda=\frac{1}{15}\).

(a) Write down the probability distribution of the waiting time until 3 customers have asked about the book Home Engineering.

(b) What is the probability that you must wait more than 30 minutes before 3 customers have asked about the book Home Engineering? Calculate in both of the following ways.

- Calculate directly on the distribution itself.

- Calculate by using the Normal approximation.

(c) What is the probability that precisely \(m\) customers have asked about the book during a 30 minute time period?

(d) What is the expected number of customers who have asked about the book during the period?