Question

[4H-16] A bottle of orange juice is being filled by machine. Amount dispensed by the machine is known to be approximately normally distributed with mean of 10 ounces and standard deviation of m ounces. If we want to make sure that proportion of the bottles filled over 12 ounces to be 10%, what does the value of m have to be? (Round to 2 decimals.)

Answer 1

Answer:1.5625

Explanation:

Given

mean
`\mu =10 ounces`

standard deviation
`\sigma =m ounces`

For bottles to be filled over 12 ounces i.e. area right to the bell curve for z score

and area left side of the z score is 1-0.1=0.9

so value close to 0.9 in standard normal curve which is 0.8997

z score corresponding to 0.8997 is 1.28

also z score for 12 ounce

`z=(x-\mu )/(\sigma )`

`z=(12-10)/(m)`

`1.28=(2)/(m)`

`m=(2)/(1.28)`

`m=1.5625`