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=(X-\mu)/(\sigma)`

For X = 11.5

`z=(11.5-11.7)/(0.2)\approx-1`

For X = 11.6

`z=(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