The distribution of the number of dill pickle spears in a gallon container is approximately Normal with mean 110 and standard deviation 10.
Approximately what percent of the containers had fewer than 105 spears?
A) -50 percent
B) 50 percent
C) 30.85 percent
D) 69.15 percent
E) -30.85 percent

Question

Quizplus · Accepted Answer

To find the percentage of containers with fewer than 105 spears, we calculate the Z-score for 105 spears using the formula Z = (X - μ) / σ, where X is the value (105 spears), μ is the mean (110 spears), and σ is the standard deviation (10). This gives us Z = (105 - 110) / 10 = -0.5. Looking up a Z-score of -0.5 in a standard normal distribution table or using a calculator, we find that approximately 30.85% of the containers had fewer than 105 spears.

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