Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes.

Answer 1

Answer: 0.025

Explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between interval : [45.0 minutes, 55.0 minutes]

The probability density function will be :-

`f(x)=(1)/(b-a)=(1)/(55-45)=(1)/(10)`

The probability that a given class period runs between 51.5 and 51.75 minutes is given by :-

`P(51.5<x<51.75)=\int^(51.75)_(51.5)f(x)\ d(x)\\\\=(1)/(10)\int^(51.75)_(51.5)\ dx\\\\=(1)/(10)[x]^(51.75)_(51.5)=(1)/(10)(51.75-51.5)=0.025`

Hence, the probability that a given class period runs between 51.5 and 51.75 minutes is 0.025 .