Question

The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230. Find the probability that (a) the gross sales over the next two weeks exceeds $5000. (b) weekly sales exceed $2000 in at least 2 of the next 3 weeks.

Answer 1

(a)0.0325

(b)0.9033

Step-by-step explanation:

(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

and when we can assume that they are independent (knowing total sales in the first week does not affect total sales in the second week).

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