The daily number of customers entering a large grocery store who purchase one or more dairy products is given by the outcome of a binomial random variable X_t
with parameters p and n_t for day t. The number of customers who enter the grocery store on any given day, n_t, is itself an outcome of a random variable N_t that has
a discrete uniform distribution on the range {200,201,. . .,300}. The X_t’s and the N_t’s are jointly independent.

The local dairy products commission wants an estimate of the daily proportion of customers entering the store who purchase dairy products and wants you to use

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t=1 an outcome of Xa = (1/d) (X/N), where d is num- ber of days, as an estimate. (a) Does Xp? Does Xap? Does Xap? (b) Define an asymptotic distribution for Xa. If p = .8, 300 d=300, and n = 75,000, what is the approxi- mate probability that Xa E (.78,.82)?