Answer:
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.