Maiclubk

2021-08-22

The gross weekly sales at a certain restaurant is a normal random variable with mean $2200 and standard deviation $230.
What is the probability that
(a) the total gross sales over the next 2 weeks exceeds $5000.
(b) weekly sales exceed $2000 in at least 2 of the next 3 weeks? What independence assumptions have you made?

davonliefI

Skilled2021-08-23Added 79 answers

(a)

Define random variables X and Y that marks the total gross sales over the first and the second week, respectively.

We are given that

Know, we are considering random variable Z=X+Y. From the theory, we know that

i.e., the sum of two independent Normals is again Normal.

Now, we are required to find:

(b)

Define random variable N as the number of weeks in the next three weeks where the total gross sales exceed 2000.

We have that N~ Binom(3,p), where

Finally

Result:

(a)0.0325

(b)0.9033

22+64

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