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 51.5 and 51.75 minutes.

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between interval : [45.0 minutes, 55.0 minutes]

The probability density function will be :-

[tex]f(x)=\dfrac{1}{b-a}=\dfrac{1}{55-45}=\dfrac{1}{10}[/tex]

The probability that a given class period runs between 51.5 and 51.75 minutes is given by :-

[tex]P(51.5<x<51.75)=\int^{51.75}_{51.5}f(x)\ d(x)\\\\=\dfrac{1}{10}\int^{51.75}_{51.5}\ dx\\\\=\dfrac{1}{10}[x]^{51.75}_{51.5}=\dfrac{1}{10}(51.75-51.5)=0.025[/tex]

Hence, the probability that a given class period runs between 51.5 and 51.75 minutes is 0.025 .