Answer:
The value of mean is ![\mu = 15.64](https://tex.z-dn.net/?f=%5Cmu%20%3D%2015.64)
Step-by-step explanation:
The normal distribution of the soft-drink dispensing machine can be stated statistically like
~ ![N (\mu ,0.191^2)](https://tex.z-dn.net/?f=N%20%28%5Cmu%20%2C0.191%5E2%29)
The standard form representation is
![P(X](https://tex.z-dn.net/?f=P%28X%3Cx%29%20%3D%20P%28Z%3Cx-%20%5Cfrac%7B%5Cmu%7D%7B%5Csigma%7D%20%29)
Now we need to obtain
in such a way that
![P(X>16) = 0.01](https://tex.z-dn.net/?f=P%28X%3E16%29%20%3D%200.01)
In standard form
Since
![P(Z>16 -\frac{\mu}{0.191} ) = 0.03](https://tex.z-dn.net/?f=P%28Z%3E16%20-%5Cfrac%7B%5Cmu%7D%7B0.191%7D%20%29%20%3D%200.03)
This means
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C16%20-%20%5Cfrac%7B%5Cmu%7D%7B0.191%7D%20%29%20%3D%200.97)
Now looking at the z-table for probability of 0.99 we obtain 1.88
i.e
Making ![\mu\ the \ subject](https://tex.z-dn.net/?f=%5Cmu%5C%20the%20%5C%20subject)
![16 - \mu = 1.88 *0.191](https://tex.z-dn.net/?f=16%20-%20%5Cmu%20%3D%201.88%20%2A0.191)
![\mu = 16 -(1.88*0.191)](https://tex.z-dn.net/?f=%5Cmu%20%3D%2016%20-%281.88%2A0.191%29)
![=15.64](https://tex.z-dn.net/?f=%3D15.64)
First, find the amount of time is taken to travel 1 mile :
time taken to travel 1 mile = 20/6 = 3 ⅓ mins
hence, time taken to travel 9 miles = 3 ⅓ x 9 = 30 mins
time taken to travel 10 miles = 3 ⅓ x 10 = 33 ⅓ mins
43 ........................................
<span>Divide each side by '28'.
x = 4.25
Simplifying
x = 4.25 </span>