Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

Answer 1

Answer: 0.125

Step-by-step explanation:

Given: A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed in interval (50,52).

∴ The probability density function of X will be :-

$f(x)=\dfrac{1}{b-a}=\dfrac{1}{52-50}=\dfrac{1}{2}$

The required probability will be:-

$P(51.25<x<51.5)=\int^{51.5}_{51.25}f(x)\ dx\\\\=\dfrac{1}{2}\int^{51.5}_{51.25}\ dx\\\\=\dfrac{1}{2}[x]^{51.5}_{51.25}\\\\=\dfrac{1}{2}(51.5-51.25)=\dfrac{0.25}{2}=0.125$

Hence, the probability that a given class period runs between 51.25 and 51.5 minutes =0.125