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

Step-by-step explanation:

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

$f(x)=\dfrac{1}{b-a}$

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 = $f(x)=\dfrac{1}{60-50}=\dfrac{1}{10}$

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

$P(50.25<x<51.5)=\int^{51.5}_{50.25}\ f(x)\ dx\\\\=\int^{51.5}_{50.25} \dfrac{1}{10}\ dx\\\\= \dfrac{1}{10}[x]^{51.5}_{50.25}\\\\=\dfrac{1}{10}(51.5-50.25)\\\\=\dfrac{1.25}{10}=0.125$

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