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?

Question

(1 point)
Responses

34%
34%

97.5%
97.5%

84%
84%

50%
50%

Answer 1

To find the percentage of onions that will be accepted by the grocery store, we need to calculate the z-score of 3 inches (the minimum diameter required for acceptance).

z = (X - μ) / σ
z = (3 - 3.25) / 0.25
z = -1

Using a z-table or a calculator, we can find that the area to the left of z = -1 is 0.1587. This represents the percentage of onions that are smaller than 3 inches in diameter.

Since we want to find the percentage that are at least 3 inches in diameter (which is the complement of smaller than 3 inches), we subtract 0.1587 from 1 to get 1 - 0.1587 = 0.8413.

Multiplying by 100% to convert to a percentage, we get 84%, so the answer is 84%.