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.
Accepted Solution
A:
Answer: 0.125Step-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 :-[tex]f(x)=\dfrac{1}{b-a}=\dfrac{1}{52-50}=\dfrac{1}{2}[/tex]The required probability will be:-[tex]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[/tex]Hence, the probability that a given class period runs between 51.25 and 51.5 minutes =0.125