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 50.25 and 50.5 minutes.

Answer 1

Answer: 0.025

Step-by-step explanation:

The probability density function for a random variable that is uniformly distributed on 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 45.0 and 55.0 minutes.

Let x be the random variable that denotes the  lengths of her classes.

Then, the probability density function = $f(x)=\dfrac{1}{55-45}=\dfrac{1}{10}$

Now, the probability that a given class period runs between 50.25 and 50.5 minutes will be :-

$P(50.25$

Hence, the required probability =0.025