Question

Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.10 ounces and a standard deviation of .04 ounces. The company is interested in reducing the amount of extra beer that is poured into the 12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by this machine. For what fill amount are they searching? Round to the nearest thousandth. Please demonstrate with TI84 steps.

Answer 1

Given that, mean = 12.10 ounces and

standard deviation = 0.04 ounces

We want to find the value of x such that, P(X>x)=.015 (1.5%)

P(X > x) = 0.015

=> 1 - P(X < x) = 0.015

=> P(X < x) = 0.985

Using TI-84 calculator we find, z-score corresponds to probability 0.985

1) press 2ND and then press VARS button

2) Then gp to invNorm and enter values as follows:

area : 0.985

: 0

: 1

paste

Then press ENTER we get, z-score = 2.17009

Now, we find, the value of x

Therefore, required amount is 12.187 ounces