Answer:
your answer is 2.83
Step-by-step explanation:
Answer:12533
Step-by-step explanation:
Step-by-step explanation:
the new points : W=(-3,5) Z (-3,3) Y°(-1,3) X=(3,5)
Given the CDF
![F_X(x)=\begin{cases}0&\text{for }x](https://tex.z-dn.net/?f=F_X%28x%29%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Dx%3C0%5C%5C1-e%5E%7B-8x%7D%26%5Ctext%7Bfor%20%7Dx%5Cge0%5Cend%7Bcases%7D)
we have PDF
![\dfrac{\mathrm dF_X(x)}{\mathrm dx}=f_X(x)=\begin{cases}0&\text{for }x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dF_X%28x%29%7D%7B%5Cmathrm%20dx%7D%3Df_X%28x%29%3D%5Cbegin%7Bcases%7D0%26%5Ctext%7Bfor%20%7Dx%3C0%5C%5C8e%5E%7B-8x%7D%26%5Ctext%7Bfor%20%7Dx%5Cge0%5Cend%7Bcases%7D)
Note that
![X](https://tex.z-dn.net/?f=X)
is wait-time given in hours, so we need to convert from minutes to hours:
![12\text{ min}\times\dfrac{1\text{ hr}}{60\text{ min}}=\dfrac15\text{ hr}](https://tex.z-dn.net/?f=12%5Ctext%7B%20min%7D%5Ctimes%5Cdfrac%7B1%5Ctext%7B%20hr%7D%7D%7B60%5Ctext%7B%20min%7D%7D%3D%5Cdfrac15%5Ctext%7B%20hr%7D)
so we're looking for
![\mathbb P\left(X](https://tex.z-dn.net/?f=%5Cmathbb%20P%5Cleft%28X%3C%5Cdfrac15%5Cright%29)
.
The CDF gives us this value right away, since
![F_X(x)=\mathbb P(X](https://tex.z-dn.net/?f=F_X%28x%29%3D%5Cmathbb%20P%28X%3Cx%29%3D%5Cmathbb%20P%28X%5Cle%20x%29)
for any continuous random variable
![X](https://tex.z-dn.net/?f=X)
with distribution function
![F_X(x)](https://tex.z-dn.net/?f=F_X%28x%29)
:
![\mathbb P\left(X](https://tex.z-dn.net/?f=%5Cmathbb%20P%5Cleft%28X%3C%5Cdfrac15%5Cright%29%3DF_X%5Cleft%28%5Cdfrac15%5Cright%29%3D1-e%5E%7B-8%2F5%7D%5Capprox0.7981)
To use the PDF, we need to integrate: