Answer: 0.025
Step-by-step explanation:
The probability density function for a random variable that is uniformly distributed on interval [a,b] is given by :-
[tex]f(x)=\dfrac{1}{b-a}[/tex]
Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes.
Let x be the random variable that denotes the lengths of her classes.
Then, the probability density function = [tex]f(x)=\dfrac{1}{55-45}=\dfrac{1}{10}[/tex]
Now, the probability that a given class period runs between 50.25 and 50.5 minutes will be :-
[tex]P(50.25<x<50.5)=\int^{50.5}_{50.25}\ f(x)\ dx\\\\=\int^{50.5}_{50.25}\ \dfrac{1}{10}\ dx\\\\= \dfrac{1}{10}[x]^{50.5}_{50.25}\\\\=\dfrac{1}{10}[50.5-50.25]\\\\=\dfrac{1}{10}[0.25]=0.025[/tex]
Hence, the required probability =0.025
