Answer: 0.025
Step-by-step explanation:
Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between interval : [48.0 minutes, 53.0 minutes]
Let x be the lengths of her classes that are uniformly distributed between interval : [48.0 minutes, 53.0 minutes].
The probability density function for the given situation :-
[tex]f(x)}=\dfrac{1}{55-45}=\dfrac{1}{10}[/tex]
The probability that a given class period runs between 51.25 and 51.5 minutes is given by :-
[tex]P(51.25<x<51.5)=\int^{51.5}_{51.255}f(x)\ d(x)\\\\=\dfrac{1}{10}\int^{51.5}_{51.25}\ dx\\\\=\dfrac{1}{10}[x]^{51.5}_{51.25}\\\\=\dfrac{1}{10}(51.5-51.25)\\\\=\dfrac{1}{10}(0.25)\\\\=0.025[/tex]
Hence, the probability that a given class period runs between 51.25 and 51.5 minutes is 0.025 .
