Question

The average height of sunflowers in a field is 64 in. with a standard deviation of 3.5 in. On a piece of paper, draw a normal curve for the distribution, including the values on the horizontal axis at one, two, and three standard deviations from the mean. Describe your drawing in as much detail as possible, and explain how you came up with each of your labels.

b) If there are 3,000 plants in the field, approximately how many will be taller than 71 in.? Explain how you got your answer.

Answer 1

[AI-generated answer — Bot GPT 3.5]

a) The normal curve should be centered at the mean height of 64 in. The horizontal axis should be labeled with values at one, two, and three standard deviations from the mean. One standard deviation above the mean would be at 64 + 3.5 = 67.5 in, and one standard deviation below the mean would be at 64 - 3.5 = 60.5 in. Two standard deviations above the mean would be at 64 + 2(3.5) = 71 in, and two standard deviations below the mean would be at 64 - 2(3.5) = 57 in. Three standard deviations above the mean would be at 64 + 3(3.5) = 74.5 in, and three standard deviations below the mean would be at 64 - 3(3.5) = 57.5 in.

b) To find the number of sunflowers taller than 71 in, we first need to find the z-score for 71 in.

z = (X - μ) / σ
z = (71 - 64) / 3.5
z ≈ 2

Using a standard normal distribution table, we can find that the probability of a sunflower being taller than 71 in is approximately 0.0228.

So, the number of sunflowers taller than 71 in in a field of 3,000 plants would be approximately 0.0228 * 3000 ≈ 68.4, which we can round up to 69 sunflowers.