Question

The production department of the newspaper has embarked on aquality improvement effort. Its first project relates to theblackness of the newpaper print. Each day, a determinationneeds to be made concerning how black the newspaper isprinted. Blackness is measured on a standard scale in whichthe target value is 1.0. Data collected over the past yearindicate that the blackness is normally distributed with a mean of1.005 and a standard deviation of 0.10. Each day, one spot onthe first newspaper printed is chosen, and the blackness of thespot is measured. The blackness of the newspaper isconsidered acceptable if the blackness of the spot is between 0.95 and 1.05.

Assuming that the distribution has not changed from what itwas in the past year, what is the probability that the blackness ofthe spot is:

a. between 0.95 and 1.0?

b. less than 0.95 or greater than 1.05?

c. The objective of the production team is to reduce theprobability that the blackness is below 0.95 or above 1.05. Should the team focus on process improvement that lowers the meanto the target value of 1.0 or on process improvement that reducesthe standard deviation of 0.075? Justify quantitatively.

d. Each day, a sample of 25 printed spots is chosen and the blackness of the spots is measured. Assuming that the distribution of the blackness has not changed from what it was previously, what is the probability that the average blackness of the spots is less than 0.95 or greater than 1.05?

Answer 1