Question

The AMS technical services department 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 which the target value is 1.0. Data collected over the past year indicate 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 between 0.95 and 1.05.

1. Assuming that 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. between 1.0 and 1.05?
d. less than 0.95 or greater than 1.05?

2.) 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 1.05 or on process improvement that reduces the standard deviation of the upload speed to 0.075? Explain

Answer 1

Answer:-

Given That:-

The AMS technical services department 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 which the target value is 1.0. Data collected over the past year indicate 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 between 0.95 and 1.05.

1. Assuming that 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?

P(X < 1)

= 0.4801

P(X < 1) = 0.4801

b. between 0.95 and 1.0?

P(0.95 < X < 0.1)

= 0.4801 - 0.2912

= 0.1889

P(0.95 < X < 0.1) = 0.1889

c. between 1.0 and 1.05?

P(1 < X < 1.05)

= 0.6736 - 0.4801

= 0.1935

P(1 < X < 1.05) = 0.1935

d. less than 0.95 or greater than 1.05?

P(X < 0.95) + p(X > 1.05)

= 0.2912 + (1 - 0.6736)

= 0.6176

P(X < 0.95) + p(X > 1.05) = 0.6176

2.) 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 1.05 or on process improvement that reduces the standard deviation of the upload speed to 0.075?

If mean increases to 1.05, then the probability will be

P(X < 1)

= 0.3085

P(X < 1) = 0.3085

If the standard deviation reduces to 0.075, then the probability will be

P(X < 1)

= 0.4721

P(X < 1) = 0.4721

The probability in part(a) will be very less deviate from the probability by reducing the standard deviation and more deviate from the probability by increasing the mean.

Since the probability by increasing the mean will be less than the probability by reducing the standard deviation, so the team should focus on process improvement that increases the mean upload speed.