Question

A vending machine dispenses coffee into a twelve ounce cup he amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.006 ounce. You can allow the cup to overfill 4â% of the time. What amount should you set as the mean amount of coffee to beâ dispensed?

Answer 1

Answer:

this mean amount of coffee to be dispensed would be 11.99, approximately 12

Step-by-step explanation:

first of all we have this information available to answer this question.

standard deviation σ = 0.006 ounces

prob(x > 12) = 0.04

we use this formular to find the mean

z = x - μ/σ

 the value of the z score at 4% is equal to 1.7507

such that

$1.7507 = \frac{12-u}{0.006}$

we cross multiply from this stage

1.7507*0.006 = 12-μ

0.0105042 = 12-μ

μ = 12 - 0.0105042

herefore, the mean amount μ = 11.99 this can be approximated to 12