The production department of the newspaper has embarked on a quality improvement effort. Its first project relates to the blackness of the newspaper print. Each day, a determination needs to be made concerning how black the newspaper is printed. Blackness is measured on a standard scale in which the target value is 1.0. Data collected over the past year indicate that the blackness is approximately normally distributed, with a mean of 1.005 and a standard deviation of 0.10. Each day, one spot on the first newspaper printed is chosen, and the blackness of the spot is measured. The blackness of the newspaper is considered acceptable if the blackness of a spot is between 0.95 and 1.05.
(a) Assuming that the distribution has not changed from what it was in the past year, what is the probability that the blackness of the spot is
a. Less than 1.0?
b. Between 0.95 and 1.0?
c. Between 1.0 and 1.05?
d. Less than 0.95 or greater than 1.05?
(b) The objective of the production team is to reduce the probability that the blackness is below 0.95 or above 1.05. Should the team focus on process improvement that lowers the mean to the target value of 1.0 or on process improvement that reduces the standard deviation to 0.075? Explain.
Continuing its quality improvement effort first described in the Chapter 6 “Managing the Springville Herald” case, the production department of the newspaper has been monitoring the blackness of the newspaper print. As before, blackness is measured on a standard scale in which the target value is 1.0. Data collected over the past year indicate that the blackness is approximately normally distributed, with a mean of 1.005 and a standard deviation of 0.10. SH.7 Each day, 25 spots on the first newspaper printed are chosen, and the blackness of the spots is measured. Assuming that the distribution has not changed from what it was in the past year, what is the probability that the mean blackness of the spots is a. Less than 1.0? b. Between 0.95 and 1.0? c. Between 1.0 and 1.05? d. Less than 0.95 or greater than 1.05? e. Suppose that the mean blackness of today’s sample of 25b spots is 0.952. What conclusions can you reach about the blackness of today’s newspaper based on this result? Explain.
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