Answer:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
Step-by-step explanation:
We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:
[tex] X \sim Unif (a= 8, b=22)[/tex]
And for this case we want to find the following probability:
[tex] P(X>14)[/tex]
We can find this probability using the complement rule and the cumulative distribution function given by:
[tex] P(X<x) = \frac{x-a}{b-a} ,a \leq x \leq b[/tex]
Using this formula we got:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
