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 51.25 and 51.5 minutes.

Answer 1

0.025

Explanation:

Given that a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes

Let X be the length of the class of statistics professor

X is U(46,56)

We are to find the probability that a given class period runs between 51.25 and 51.5 minutes.

The pdf of X is =
`(1)/(56-46) =0.1, 46\leq x\leq 56`

Using this we can find probability using integration

`P(51.25\leq x\leq 51.5)`

=
`\int\limits^(51.5) _(51.25) 0.1 \, dx \\=0.1(51.5-51.25)\\= 0.025`