A grocery store will only accept yellow onions that are at least 3 inches in diameter. A grower has a crop of onions with diameters that are normally distributed with a mean diameter of 3.25 inches and a standard deviation of 0.25 inches. What percent of the onions will be accepted by the grocery store?

(1 point)
Responses

34%
34%

97.5%
97.5%

84%
84%

50%

1 answer

To find the percentage of onions that will be accepted by the grocery store, we need to determine the percentage of onions that have a diameter of at least 3 inches.

Using the Z-score formula:
Z = (X - μ) / σ

Where:
X = 3 inches (minimum diameter required by the grocery store)
μ = 3.25 inches (mean diameter)
σ = 0.25 inches (standard deviation)

Z = (3 - 3.25) / 0.25
Z = -0.25 / 0.25
Z = -1

Looking up the Z-score in a standard normal distribution table, we find that the percentage of onions with a diameter of at least 3 inches is approximately 84%.

Therefore, the correct answer is:
84%