Solve the problem.
-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 12.14 ounces and a standard
Deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.04 ounces of beer.
A) 0.4938
B) 0.9938
C) 0.0062
D) 0.5062

Question

Quizplus · Accepted Answer

We need to find the probability that a bottle contains fewer than 12.04 ounces of beer.

First, we standardize the value of 12.04 using the formula:

z = (x - μ) / σ

where:
x = 12.04
μ = 12.14
σ = 0.04

z = (12.04 - 12.14) / 0.04 
z = -2.5

Next, we look up the probability corresponding to z = -2.5 in the standard normal distribution table.

The table gives us a probability of 0.0062. Therefore, the probability that a bottle contains fewer than 12.04 ounces of beer is 0.0062.

Hence, the answer is C.

Solve the Problem. -Suppose a Brewery Has a Filling Machine That Fills 12