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sighgabbie
20.02.2021 •
Mathematics
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Ответ:
70 sorry if wrong
Step-by-step explanation:
Ответ:
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![X=X_1+X_2](/tpl/images/0366/1410/e5607.png)
Assuming that
and
follows same distribution with same mean and deviation.
So,![X\sim N(4400,230\sqrt{2})](/tpl/images/0366/1410/a3bc3.png)
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,![P(Y\geq 2)](/tpl/images/0366/1410/77ea6.png)
So,![P(Y\geq 2)=P(Y=2)+P(Y=3)](/tpl/images/0366/1410/ffb01.png)
The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.