Question

The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. If one such class is randomly selected, find the probability that the class length is more than 53.1 min. PX < 53.1)

Answer 1

`P(X>53.1) = 1-(53.1-49.2)/(55.5-49.2)= 1-0.619 = 0.381`

And
`P(X<53.1) = 0.619`

Explanation:

Let X the random variable who represent the lengths of a professor's classes and we know that the distribution for X is given by:

`X \sim Unif (a=49.2, b=55.5)`

And for this case we want to find the following probability:

`P(X>53.1)= 1- P(x<53.1)`

We can use the cumulative distribution function given by:

`F(x) =(x-a)/(b-a) , a\leq x \leq b`

And if we use this formula and the complement rule we got :

`P(X>53.1) = 1-(53.1-49.2)/(55.5-49.2)= 1-0.619 = 0.381`

And
`P(X<53.1) = 0.619`