Question

The amount of time, in minutes, that a woman must wait for a cab is uniformly distributed between zero and 12 minutes, inclusive. What is the probability that a person waits fewer than 11 minutes

Answer 1

`P(X\leq x) =(x-a)/(b-a), a \leq x \leq b`

And using this formula we have this:

`P(X<11) = (11-0)/(12-0)= 0.917`

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

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:

`X \sim Unif (a=0, b =12)`

And we want to find the following probability:

`P(X<11)`

And for this case we can use the cumulative distribution function given by:

`P(X\leq x) =(x-a)/(b-a), a \leq x \leq b`

And using this formula we have this:

`P(X<11) = (11-0)/(12-0)= 0.917`

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917