The quality specification for a certain manufactured compone

The quality specification for a certain manufactured component is that the pressure at a certain point must not exceed 30 pounds. A manufacturer who would like to enter this market finds that he can make components with a mean pressure µ= 28 lbs, but the pressure varies from one specimen to the next with a standard deviation of = 1.6 lbs. What proportion of his/her specimens will fail to meet the quality specification?

Solution

Mean =28 and standard deviation = 1.6

proportion of his/her specimens will fail to meet the quality specification=P(X>30) = P(Z> (30-28)/1.6)

=P(Z>1.25) = 1- P(Z<=1.25) = 1-0.89435=0.10565