Question

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 50.3 min.
P(X > 50.2) = ________.
(Report answer accurate to 2 decimal places.)

Answer 1

Answer:

P(X > 50.3) = 0.85

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.

This means that $a = 50, b = 52$

If one such class is randomly selected, find the probability that the class length is more than 50.3 min.

$P(X > 50.3) = \frac{52 - 50.3}{52 - 50} = 0.85$

So

P(X > 50.3) = 0.85