Question

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 113 cm and a standard deviation of 4.9 cm.

A. Using Excel, find the probability that one selected subcomponent is longer than 115 cm.

Probability =

B. Using Excel, find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 115 cm.

Probability =

Answer 1

A)

Go to formulas section in menu bar----select more functions -- select norm. Dist --enter the values (x=115, mean=113, std deviation=4.9 ,cumulative =1)--press enter

You will get the value of P(x<115)

But we need P(x>115) here which is equal to 1-P(x<115)

= 1-0.658423= 0.341577

B)

Here ,we will use sample std deviation = 4.9/ sqrt(3) = 2.83

The rest of input data will be same as part (a)

And follow the same procedure as used above

So the answer you should get is (1- 0.760128) = 0.239872