Question

a) 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)

To draw a normal curve for the distribution of sunflower heights, we start by placing the average height of 64 in. at the center of the curve. Then, we mark one standard deviation above and below the mean, which would be 64 + 3.5 = 67.5 in. and 64 - 3.5 = 60.5 in. respectively. Next, we mark two standard deviations above and below the mean, which would be 71 in. and 57 in. Finally, we mark three standard deviations above and below the mean, which would be 74.5 in. and 53.5 in.

b)
To determine how many plants will be taller than 71 in., we calculate the z-score for a height of 71 in. using the formula z = (x - μ) / σ, where x is the height, μ is the mean (64 in.), and σ is the standard deviation (3.5 in.).
z = (71 - 64) / 3.5 = 2
Next, we look up the z-score of 2 in a standard normal distribution table to find out the proportion of plants taller than 71 in. We find that the proportion is approximately 0.0228 or 2.28%.

Finally, to find the number of plants taller than 71 in., we multiply the proportion by the total number of plants in the field:
Number of plants = 0.0228 * 3000 = 68.4
So, approximately 68 plants will be taller than 71 in.

Answer 2

use simpler terms

Answer 3

[AI-generated answer — Bot GPT 3.5]

a) To draw the normal curve, first, mark the average height of 64 in. in the middle. Then, mark 3.5 in. above and below the average. Next, mark 7 in. above and below the average. Lastly, mark 10.5 in. above and below the average.

b) To find how many plants will be taller than 71 in., calculate the z-score for 71 in. using the formula z = (71 - 64) / 3.5 = 2.

Next, look up the z-score of 2 on a standard normal distribution table, which shows that about 2.28% of plants will be taller than 71 in.

Finally, multiply 2.28% by the total number of plants, 3000, to find that around 68 plants will be taller than 71 in.