A statistics professor plans classes so carefully so that the lengths of her cla

Question

A statistics professor plans classes so carefully so that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given period runs between 50.75 and 51.5 minutes. Round to three decimal places as needed. A statistics professor plans classes so carefully so that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given period runs between 50.75 and 51.5 minutes. Round to three decimal places as needed.

Explanation / Answer

Since this distribution runs from 46.0 to 56.0 minutes, it has a range of 10.0 (56.0-46.0). The density must be 1/10 = 0.1, so that 10.0*0.1 = 1.0.

To find the probability of being between two numbers multiply the range between the numbers by the probability density.

range: 51.5-50.75 = 0.75

0.75*0.1 = 0.075

P(50.5 < x < 50.75) = 0.075

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