The diameter of a mason jar is 3 inches but can be as large as 3.03 inches and as small as 2.97 inches. Twenty-five samples of mason jars are taken and it is discovered that these components have a grand mean of 3.01 inches and a standard deviation of 0.02 inches. What is the probability of producing a bad product?
A) 0.60
B) 0.18
C) 0.33
D) 0.45
E) 0.84

Question

Quizplus · Accepted Answer

The probability of producing a bad product can be calculated using the standard normal distribution. The z-scores for the limits (2.97 and 3.03) are calculated using the formula z = (X - μ) / σ, where X is the limit, μ is the mean, and σ is the standard deviation. The z-scores are approximately -2 and 1. The probability of a z-score being between -2 and 1 is about 0.8185, so the probability of being outside this range (producing a bad product) is 1 - 0.8185 = 0.1815, which is approximately 0.18.

The Diameter of a Mason Jar Is 3 Inches but Can