Answer: 0.025
Explanation:
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 :-

The probability that a given class period runs between 51.5 and 51.75 minutes is given by :-
![P(51.5<x<51.75)=\int^(51.75)_(51.5)f(x)\ d(x)\\\\=(1)/(10)\int^(51.75)_(51.5)\ dx\\\\=(1)/(10)[x]^(51.75)_(51.5)=(1)/(10)(51.75-51.5)=0.025](https://img.qammunity.org/2020/formulas/mathematics/high-school/mcmnll8chejg9w8oqnn3qltsfcq8w4exs0.png)
Hence, the probability that a given class period runs between 51.5 and 51.75 minutes is 0.025 .