Question

The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. If one such class is randomly selected, find the probability that the class length is more than 53.1 min. PX < 53.1)

Answer 1

Answer:

$P(X>53.1) = 1-\frac{53.1-49.2}{55.5-49.2}= 1-0.619 = 0.381$

And $P(X$

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:

$X \sim Unif (a=49.2, b=55.5)$

And for this case we want to find the following probability:

$P(X>53.1)= 1- P(x$

We can use the cumulative distribution function given by:

$F(x) =\frac{x-a}{b-a} , a\leq x \leq b$

And if we use this formula and the complement rule we got :

$P(X>53.1) = 1-\frac{53.1-49.2}{55.5-49.2}= 1-0.619 = 0.381$

And $P(X$