Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

Answer 1

Answer: 0.125

Explanation:

Given: A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed in interval (50,52).

∴ The probability density function of X will be :-

`f(x)=(1)/(b-a)=(1)/(52-50)=(1)/(2)`

The required probability will be:-

`P(51.25<x<51.5)=\int^(51.5)_(51.25)f(x)\ dx\\\\=(1)/(2)\int^(51.5)_(51.25)\ dx\\\\=(1)/(2)[x]^(51.5)_(51.25)\\\\=(1)/(2)(51.5-51.25)=(0.25)/(2)=0.125`

Hence, the probability that a given class period runs between 51.25 and 51.5 minutes =0.125