Answer:
![P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b](https://tex.z-dn.net/?f=%20P%28X%5Cleq%20x%29%20%3D%5Cfrac%7Bx-a%7D%7Bb-a%7D%2C%20a%20%5Cleq%20x%20%5Cleq%20b)
And using this formula we have this:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C11%29%20%3D%20%5Cfrac%7B11-0%7D%7B12-0%7D%3D%200.917)
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:
![X \sim Unif (a=0, b =12)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Unif%20%28a%3D0%2C%20b%20%3D12%29)
And we want to find the following probability:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C11%29)
And for this case we can use the cumulative distribution function given by:
![P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b](https://tex.z-dn.net/?f=%20P%28X%5Cleq%20x%29%20%3D%5Cfrac%7Bx-a%7D%7Bb-a%7D%2C%20a%20%5Cleq%20x%20%5Cleq%20b)
And using this formula we have this:
![P(X](https://tex.z-dn.net/?f=%20P%28X%3C11%29%20%3D%20%5Cfrac%7B11-0%7D%7B12-0%7D%3D%200.917)
Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917
Answer:
10
Step-by-step explanation: