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 111 cm and a standard deviation of 5.5 cm.

A. Using Excel, find the probability that one selected subcomponent is longer than 113 cm.

Probability =

B. Using Excel, find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 113 cm.

Probability =

Answer 1

Given data,

mean = 111 cm

standard deviation = 5.5 cm

A)

Go to formulas section in menu bar----select more functions -- select NORMDIST enter the values (x=113, mean=111, std deviation=5.5 ,cumulative =1)--press enter

You will get the value of P(x<113)

But we need P(x>113) here which is equal to 1-P(x<113)

= 1-0.641935 = ' 0.358065 ' .

B)

Here ,we will use sample std deviation = 5.5/ sqrt(3) = 5.5/1.732 = 3.17.

by using the same method from above part (a)

as NORMDIST(x=113, mean=111, std deviation=3.17 ,cumulative =1)--- press enter then we get 0.735952

the answer you should get is (1- 0.735952) = ' 0.264048 ' .