The gross weekly sales at a certain restaurant are 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?

a) The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

Step-by-step explanation:

Given : The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230.

To find : 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?

Solution :

Let and denote the sales during week 1 and 2 respectively.

a) Let

Assuming that and follows same distribution with same mean and deviation.

So,

The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The probability that sales exceed teh 2000 and amount in at least 2 and 3 next week.

We use binomial distribution with n=3.

Let Y be the number of weeks in which sales exceed 2000.

Now,

So,  

The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

7/2

(decimal: 3.5)

welcome ; )

step-by-step explanation: