You examine historical data and nd that the wait time in a queue has an exponential distribution with an average time of 5 minutes. The graph of the density function for an exponentialis plotted below, with the red vertical line indicating the mean of the density function.

Note: If X~Exponential(r);E(X)=r, V(X)=r^2

(a) TRUE/FALSE and explain your choice: According to Central Limit Theorem,

X mean 5 will have an approximately normal distribution.

(b) What is the probability that you will observe a sample mean between 4 and 6

if you have a random sample of size n =49? Justify your calculation and explicitly state the distribution used.