Answer:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]
Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917
Step-by-step explanation:
Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:
[tex] X \sim Unif (a=0, b =12)[/tex]
And we want to find the following probability:
[tex] P(X<11)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]
Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917
