Using the uniform distribution, it is found that:
a) There is a 0.3333 = 33.33% probability that the friend is between 10 and 20 minutes late.
b) Within 9 minutes.
What is the uniform probability distribution?
It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Researching the problem on the internet, it is found that the variable is uniform with a = 0 and b = 30.
Item a:
[tex]P(10 \leq X \leq 20) = \frac{20 - 10}{30 - 0} = 0.3333[/tex]
There is a 0.3333 = 33.33% probability that the friend is between 10 and 20 minutes late.
Item b:
This is x for which P(X < x) = 0.3, hence:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]0.3 = \frac{x}{30}[/tex]
[tex]x = 9[/tex]
Within 9 minutes.
To learn more about the uniform distribution, you can check https://brainly.com/question/13889040
