AP Statistics Question

Question

Suppose the average height of sunflowers is 16 inches, with a standard deviation of 2. And the average height of roses is 12 inches, with a standard deviation of 3. Using a normal model, how would I find the percent of sunflowers expected to be taller than roses?

Answer 1

Choose a specific height of 20 inches for both sunflowers and roses.

For sunflowers, the normal test statistic will be (20 − 16) ÷ 2 or Z = 2 which

returns a probability under the standard normal curve as 0.4772498681.

For roses, the normal test statistic will be (20 − 12) ÷ 3 or Z = 8/3 which

returns a probability under the standard normal curve as 0.4961696194.

For a random sample of 100 sunflowers, 100(1 − 0.4772498681) or

52.27501319 sunflowers will be taller than 20 inches.

For a random sample of 100 roses, 100(1 − 0.4961696194) or

50.38303806 roses will be taller than 20 inches.

Then (52.27501319 − 50.38303806) / 100 or 1.891975133%

(roughly 1.9%) more sunflowers than roses will be taller than

20 inches.