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Probability Under the Curve of the Standard Normal Distribution

Upload speed are measured on a standard scale I which the target value is 1.0. Data collected over the past year indicate that the upload speeds are approximately normally distributed with a means of 1.005 and a standard deviation of 0.10. Each day at 25 random times , the upload speed is measured . 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) P( < 1.0) =

(b) P(0.95 < < 1.0)

(c) P(1.0 < < 1.05)

(d) P( < 0.95) or P( > 1.05)

(e) Type a substantive answer to the question.

Solution Preview

Now z=(x-u)/sd=(x-1.005)/0.10

(a) P(X<1.0)=P(Z<(1.0-1.005)/0.10)=P(Z<-0.05)=0.4801 from standard normal table.

(b) ...

Solution Summary

The solution gives detailed steps on calculating the probability under the curve of the standard normal distribution. All formulas and calculations are shown and explained.