In just a couple sentences answer the following questions
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.
a) The normal curve on the paper would show a symmetrical distribution with the mean at 64 in. and the standard deviations at 60.5 in., 67.5 in., and 71 in. The labels were calculated by adding or subtracting the standard deviation from the mean to show one, two, and three standard deviations from the mean.
b) To calculate the approximate number of plants taller than 71 in., you can use the Z-score formula: Z = (X - μ) / σ. Plugging in the values (X = 71 in., μ = 64 in., σ = 3.5 in.), you can find the Z-score and then use a Z-score table or calculator to find the proportion of plants taller than 71 in. Then, multiply that proportion by the total number of plants (3,000) to find the approximate number of plants taller than 71 in.