The number of applications a vendor sells per day on Google Play, X, can be modeled by a Poisson distribution with mean = 16, i.e. X P ois( = 16).

(a)Find the mean and standard deviation of X.

(b)Suppose the vendor records the daily sales over a 30 day period. If X equals the mean number of daily sales over this 30 day period, determine the approximate distribution of X . Be sure to state all parameters.

(c) Suppose the vendor records their sales over a 30 day period. If X equals the mean number of daily sales over this 30 day period, determine the probability that X is greater than 15.

(d) Suppose the vendor records their sales over a 30 day period. Approximate the 95th percentile of the mean daily sales X .

(e) Approximate the probability that the vendor sells more than 6000 applications in 1 year. Hint: Restate this problem in terms of the sample mean X .