At a certain coffee shop all the customers buy a cup of coff

At a certain coffee shop, all the customers buy a cup of coffee and some also buy a donut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 340 cups and a standard deviation of 25 cups. He also believes that the number of donuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 160 donuts and a standard deviation of 13.

-The shop is open every day but Sunday. Assuming day-to-day sales are independent, what\'s the probability he\'ll sell over 2000 cups of coffee in a week?

Solution

Here, it is like asking the average is over 2000/6 = 333.3333333. (Open only for 6 days)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    333.33333      
u = mean =    340      
n = sample size =    6      
s = standard deviation =    25      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.653197591      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.653197591   ) =    0.743185549 [ANSWER]