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

Answer:

0.025

Step-by-step 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 = $\frac{1}{56-46} =0.1, 46\leq x\leq 56$

Using this we can find probability using integration

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

=$\int\limits^{51.5} _{51.25} 0.1 \, dx \\=0.1(51.5-51.25)\\= 0.025$