Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 60.0 minutes. Find the probability that a given class period runs between 50.25 and 51.5 minutes.

Answer 1

Answer: 0.125

Explanation:

The probability density function for a uniformly distributed function in interval [a,b] is given by :-

`f(x)=(1)/(b-a)`

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 60.0 minutes.

Let x denotes the lengths of classes.

Then, Density function =
`f(x)=(1)/(60-50)=(1)/(10)`

Now, the probability that a given class period runs between 50.25 and 51.5 minutes is given by :_

`P(50.25<x<51.5)=\int^(51.5)_(50.25)\ f(x)\ dx\\\\=\int^(51.5)_(50.25) (1)/(10)\ dx\\\\= (1)/(10)[x]^(51.5)_(50.25)\\\\=(1)/(10)(51.5-50.25)\\\\=(1.25)/(10)=0.125`

Hence, the probability that a given class period runs between 50.25 and 51.5 minutes = 0.125