Find and Interpret the Area under a Normal Curve
-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 12.43 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.33 ounces of beer.
A) 0.0062
B) 0.4938
C) 0.9938
D) 0.5062

Question

Quizplus · Accepted Answer

To find the probability that a bottle contains fewer than 12.33 ounces, we calculate the Z-score for 12.33 ounces using the formula Z = (X - μ) / σ, where X is the value (12.33 ounces), μ is the mean (12.43 ounces), and σ is the standard deviation (0.04 ounce). This gives us Z = (12.33 - 12.43) / 0.04 = -2.5. Looking up the Z-score of -2.5 in the standard normal distribution table or using a calculator, we find the probability is approximately 0.0062. This means there is a 0.62% chance a bottle contains fewer than 12.33 ounces of beer.

Find and Interpret the Area Under a Normal Curve