A biologist found the wingspans of a group of Monarch butterflies to be normally distributed with a mean of 51.7 mm and a standard deviation of 2.2 mm. What percent of the butterflies had the following wingspans? (Round your answers to one decimal place.)

(a) Less than 48.7 mm

A. 12.4%
B. 21.2%
C. 34.1%
D. 42.7%

(b) Between 49 and 52 mm

A. 45.5%
B. 58.7%
C. 73.2%
D. 82.1%

The percentage of butterflies with wingspans less than 48.7 mm is approximately 8.6%, and the percentage of butterflies with wingspans between 49 and 52 mm is approximately 44.3%.

Explanation:

To find the percent of butterflies with wingspans less than 48.7 mm, we can use the standard normal distribution table. First, we convert the value to a z-score using the formula z = (x - mean) / standard deviation. So, z = (48.7 - 51.7) / 2.2 = -1.3636. From the table, we find that the area to the left of -1.3636 is 0.0859, or 8.6%. Therefore, the percentage of butterflies with wingspans less than 48.7 mm is approximately 8.6%, which is not one of the given options.

To find the percent of butterflies with wingspans between 49 and 52 mm, we calculate the z-scores for both values. The z-score for 49 mm is (49 - 51.7) / 2.2 = -1.2273, and the z-score for 52 mm is (52 - 51.7) / 2.2 = 0.1364. From the standard normal distribution table, we find that the area to the left of -1.2273 is 0.1099, and the area to the left of 0.1364 is 0.5524. Therefore, the percentage of butterflies with wingspans between 49 and 52 mm is 55.24% - 10.99% ≈ 44.3%, which is not one of the given options.

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