A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a
crop of onions with diameters that are normally distributed with a mean diameter of 3.25 in. and a
standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?
(1 point)
34%
97.5%
84%
50%
To find the percentage of onions that will be accepted by the grocery store, we need to find the percentage of onions with a diameter of at least 3 inches.
To do this, we first need to find the z-score for a diameter of 3 inches using the formula:
z = (X - μ) / σ
Where X is the diameter we are interested in (3 inches), μ is the mean diameter (3.25 inches), and σ is the standard deviation (0.25 inches).
z = (3 - 3.25) / 0.25
z = -0.25 / 0.25
z = -1
Next, we use a standard normal distribution table or calculator to find the percentage of values below a z-score of -1. This percentage is 0.1587 or 15.87%.
However, because we are looking for the percentage of values above a z-score of -1 (since the grocery store only accepts onions with a diameter greater than or equal to 3 inches), we need to subtract 0.1587 from 1, giving us:
1 - 0.1587 = 0.8413 or 84.13%
Therefore, approximately 84% of the onions will be accepted by the grocery store.
Therefore, the answer is:
84%