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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

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Answer:

0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value between c and d is:


P(c \leq X \leq d) = (d - c)/(b - a)

Uniformly distributed between 47.0 and 57.0 minutes.

This means that
a = 47, b = 57

Find the probability that a given class period runs between 51.25 and 51.5 minutes.


P(c \leq X \leq d) = (51.5 - 51.25)/(57 - 47) = 0.025

0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.

User BenjaminB
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