The distribution of the number of dill pickle spears in a gallon container is approximately Normal with mean 110 and standard deviation 10.
If a container had to have at least 90 spears to pass quality control, approximately what percent of the containers failed? (That is, had fewer than 90 spears)?
A) 2.5 percent
B) 5 percent
C) 16 percent
D) 68 percent
E) 95 percent

Question

Quizplus · Accepted Answer

To find the percentage of containers that failed (had fewer than 90 spears), we calculate the Z-score for 90 spears using the formula Z = (X - μ) / σ, where X is 90, μ (mean) is 110, and σ (standard deviation) is 10. This gives us Z = (90 - 110) / 10 = -2. A Z-score of -2 corresponds to approximately 2.5% of the area under the normal distribution curve to the left, indicating that about 2.5% of the containers failed the quality control.

The Distribution of the Number of Dill Pickle Spears in a Gallon