Question

The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with a mean of 11.711.7 fluid ounces and a standard deviation of 0.20.2 fluid ounce. A drink is randomly selected. Find the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces.

Answer 1

Answer:  0.1499

Step-by-step explanation:

Given : The amounts a soft drink machine is designed to dispense for each drink are normally​ distributed, with mean $\mu=11.7\text{ fluid ounces}$

Standard deviation : $\sigma=0.2\text{ days}$

z-score : $z=\dfrac{X-\mu}{\sigma}$

For X = 11.5  

$z=\dfrac{11.5-11.7}{0.2}\approx-1$

For X = 11.6  

$z=\dfrac{11.6-11.7}{0.2}\approx-0.5$

Now, the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces will be :-

$P(11.5<X<11.6)=P(-1<z<-0.5)=P(z<-0.5)-P(z<-1)\\\\=0.3085375-0.1586553=0.1498822\approx0.1499$

Hence, the probability that the drink is between 11.511.5 and 11.611.6 fluid ounces =0.1499