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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.

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