SAMS has embarked on a quality improvement effort. Its first project relates to

Question

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.

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

Explanation / Answer

mean = 1.005

standard deviation = 0.10

a)probability that upload speed is Less than 1.0 i.e P(X<1.0)

z value of 1 is (1-1.005)/0.10 = -0.005/0.10 = -0.05 corresponding p value is 0.48

P(X<1.0) = 0.48

b)

z value of 0.95 is (0.95-1.005)/0.10 = -0.55 corresponding p value is 0.29116

P(X<0.95) = 0.29116

P(0.95<X<1) = 0.48 - 0.29116 = 0.18884

c)

z value of 1.05 is (1.05-1.005)/0.10 = 0.45 corresponding p value is 0.29116

P(X<1.05) = 0.673645

P(X<0.95 or X>1.05) = P(X<0.95)+P(X>1.05) = P(X<0.95)+1 -P(X<1.05)=0.29116+1 -0.673645 = 0.617515

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