Answer:
[tex] P(X>53.1) = 1-\frac{53.1-49.2}{55.5-49.2}= 1-0.619 = 0.381[/tex]
And [tex] P(X<53.1) = 0.619[/tex]
Step-by-step explanation:
Let X the random variable who represent the  lengths of a professor's classes and we know that the distribution for X is given by:
[tex] X \sim Unif (a=49.2, b=55.5)[/tex]
And for this case we want to find the following probability:
[tex] P(X>53.1)= 1- P(x<53.1)[/tex]
We can use the cumulative distribution function given by:
[tex] F(x) =\frac{x-a}{b-a} , a\leq x \leq b[/tex]
And if we use this formula and the complement rule we got :
[tex] P(X>53.1) = 1-\frac{53.1-49.2}{55.5-49.2}= 1-0.619 = 0.381[/tex]
And [tex] P(X<53.1) = 0.619[/tex]
