Answer:
[tex] P(x>7)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And if we use the complement rule and the before formula we have:
[tex] P(x>7) = 1- P(x<7) = 1- F(7) = 1 -\frac{7-5}{17-5}= 1- 0.1667 =0.8333[/tex]
Step-by-step explanation:
For this problem we denote the random variable X as the time, in minutes, it takes a barber to complete a haircut and the distribution for X is given by:
[tex] X \sim Unif (a=5, b=17)[/tex]
And we want to find the following probability:
[tex] P(x>7)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And if we use the complement rule and the before formula we have:
[tex] P(x>7) = 1- P(x<7) = 1- F(7) = 1 -\frac{7-5}{17-5}= 1- 0.1667 =0.8333[/tex]
