1.1 Each day, one spot on the first newspaper printed is chosen and the blacknes

Question

1.1 Each day, one spot on the first newspaper printed is chosen and the
blackness of the spot is measured. Suppose the blackness of the
newspaper is considered acceptable if the blackness of the spot is
between 0.95 and 1.05. 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?

1.2 If the objective of the production team is to reduce the probability that
the blackness is below 0.95 or above 1.05, would it be better off focusing
on process improvement that lowered the blackness to the target value of
1.0 or on process improvement that reduced the standard deviation to
0.075 ? Explain.

1.3 Each day, 25 spots on the first newspaper printed is chosen and the
blackness of the spot is measured. Assuming that the distribution has not
changed from what it was in the past year, what is the probability that
the average blackness of the spots is
(e) less than 1.0 ?
(f) between 0.95 and 1.0 ?
(g) between 1.0 and 1.05?
(h) less than 0.95 or greater than 1.05?

1.4 Suppose that the average blackness of today

Explanation / Answer

a. less than 1.0?
The normal distribution goes from left to right. So, if we want <1, we have:

z=rac{1-1.005}{.1}=-.05

Look this up in the table and we see that a z score of -.05 corresponds to .4801

A 48% probability that the blackness is less than 1.


f. between 0.95 and 1.0?

We already found 1, it is .4801

z=rac{.95-1.005}{.1}=-.55

In the table this is .2912

Since we are between, subtract the two values and get .4801-.2912=.1889

18.89% probability the blackness is between .95 and 1

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