Question

1. A coffee machine has two nozzles. It is known that the amount of coffee dispensed by the first nozzle is

approximately normally distributed with mean 7.1 oz. and standard deviation 0.41 oz. and that the amount of
coffee dispensed by the second nozzle is approximately normally distributed with mean 7.2 oz. and standard
deviation 0.33 oz. If a person is using an 8 oz. cup, which nozzle should he use to minimize the probability that the
cup will be overfilled and the coffee will spill?

Answer 1

The Second nozzle

Explanation:

Those are both normally distributed events, therefor we need to calculate Z value of both events:

First nozzle:

`z=(8-7.1)/0.41=2.20`

Second nozzle:

`z=(8-7.2)/0.33=2.42`

Probability of overfilling the cup from first nozzle:

`1-P(z)=1-P(2.20)=1-0.9861=0.0139`

Probability of overfilling the cup from second nozzle:

`1-P(z)=1-P(2.42)=1-0.9922=0.0087`

The Second nozzle has less probability to overfilling the cup.

PS. Find the z table at the attachment.