SOLUTION: Question - Restaurant records show that the total number of high quality disposable napkins used each week in their city premises follows a normal distribution with a mean of 850 n

Question 803390: Question - Restaurant records show that the total number of high quality disposable napkins used each week in their city premises follows a normal distribution with a mean of 850 napkins with a standard deviation of 24.0 napkins.
a)The restaurant manager wants to determine how many napkins to have at the beginning of the week so that there is at least a 95% chance that the restaurant will not run out. Calculate the minimum number of napkins required. Explain your reasoning.
b)The restaurant manager now wants to determine how many napkins to have at the beginning of the week so that there is at least a 99% chance that all the napkins will be used. Calculate the maximum number of napkins the restaurant should have. Explain your reasoning.
Please email me. Thank you.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
to solve these two questions, we use the z-value associated with 95% and 99% probabilities to determine the value of x
a) consult z-value for 95%, which is 1.65
now we can use the z-value calculation for 95%
1.65 = (x -850) / 24
39.6 = x -850
x = 889.6 = 890 napkins
b) 2.33 = (x -850) / 24
55.9 = x -850
x = 905.9 = 906

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