5. The objective of the operations team is to reduce the probability that the up

Question

5. The objective of the operations team is to reduce the probability that the upload speed is below 1.0. Should the team focus on process improvement that increases the mean upload speed to 1.05 or on process improvement that reduces the standard deviation of the upload speed to 0.075?
7. Compare your results in question #4 and question #6. What conclusions can you reach concerning the differences? SAMS has embarked on a quality improvement effort. Its first project relates to maintaining the target upload speed for its internet service subscribers. Upload speeds are measured on a standard scale in which the target values are 1.0. Data collected over the past year indicated that the upload speed is approximately normally distributed, with a mean of 1.005 and a standard deviation of 0.10. Each day, one upload speed is measured. The upload speed is considered acceptable if the measurement on the standard scale is between 0.95 and 1.05 4 If the distribution has not changed from what it was in the past year, what is the probablity that the upload speed is Less than 1.0? a. b. Between 095 and 1.0 C. Less than 0.95 or greater than 1.05 S. The objective of the operations team is to reduce the probability that the upload speed is below 1.0. Should the team focus on process improvement that increases the mean upload speed to 1.05 or on process improvement that reduces the standard deviation of the upload speed to 0.075? Continuing the quality improvement effort, the upload speed for SAMS internet service subscribers has been monitored. As before, upload speeds are measured on a standard scale in which the target value is 1.0. Data collected over the past year indicate that the upload speeds are approimately normally distributed, with a mean of 1.005 and a standard deviation of 0.10 6. Each day, at 25 random times, the upload speed is measured. If the distribution has not changed from what it was in the past year, what is the probability that the upload speed is a. Less than 1.0? b. Between 0,95 and 1.0 c Less than 0.95 or greater than 1.05 7, compare your results in question #4 and question #6, what conclusions can you reach concerning the differences?

Explanation / Answer

(5)

Data given is:

mean m = 1.005

Standard deviation S = 0.10

If the mean is improved so that it becomes 1.05, in that case the z-value will be:

z = (X-m)/S = (1-1.05)/0.10 = -0.5

If the standard deviation is improved so that it becomes 0.075, in that case the z-value will be:

z = (X-m)/S = (1-1.005)/0.075 = -0.067

Thus we see that we get a larger negative value in the first case. This means area to the left of the z-value will be smaller in first case.

So the team should focus on process improvement that increases the mean speed to 1.05, because in that the the probability of getting speeds less than 1 will be smaller.

(7)

In part 6, rather than taking a single reading, a sample of 25 readings is taken. So in this case a sampling distribution of sample means will be plotted, for which the standard deviation ( also called as standard error of the mean) is calculated as:

Standard error SE = S/(n^0.5)

Here S is standard deviation of original population, and n is the sample size equal to 25.

So, we see that SE = S/5

Thus the standard deviation of sampling distribution is 5 times less than that of previous case in part 4.

(a)

Since SE is smaller, we will get an even smaller value of z in this case, so the probability will be even less than before.

(b)

Since SE is smaller, we will get an even smaller value of z in this case both cases, so the probability will be even less than before.

(c)

Since SE is smaller, we will get an even smaller value of z in this case both cases, so the probability will be even less than before.

So wee see that the probability values in part 6 will be smaller than the ones obtained in part 4.

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