The length of life of a certain type of laboratory machine i

The length of life of a certain type of laboratory machine is normally distributed with mean 4.4 years and standard deviation 1.2 years. What period of time should the manufacturer give as a guarantee if the manufacturer were willing to replace 32.64% of the machines? (Please round your answer to second decimal place)

Solution

Let X has normal distribution.

notationally, X~N(4.4,1.2)

now we want to find a constant K such that

P(X<K)=0.3264

after applying inverse, we get the value of K as 3.86