Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class period runs between 50.75 and 51.25 minutes.

Answer 1

Answer: 0.05

Explanation:

Given : Interval for uniform distribution : [46.0 minutes, 56.0 minutes]

The probability density function will be :-

`f(x)=(1)/(56-46)=(1)/(10)=0.1\ \ , 46<x<56`

The probability that a given class period runs between 50.75 and 51.25 minutes is given by :-

`P(50.75<x<51.25)=\int^(51.25)_(50.75)f(x)\ dx\\\\=(0.1)[x]^(51.25)_(50.75)\\\\=(0.1)(51.25-50.75)=0.05`

Hence, the probability that a given class period runs between 50.75 and 51.25 minutes = 0.05