a) To draw a normal curve for the distribution of the heights of sunflowers in the field, we start by placing the average height of 64 in. in the center of the graph. Then, we mark one standard deviation above and below the mean at 60.5 in. and 67.5 in., respectively. Next, we mark two standard deviations above and below the mean at 57 in. and 71 in., respectively. Finally, we mark three standard deviations above and below the mean at 53.5 in. and 74.5 in., respectively.
b) To find out how many sunflowers will be taller than 71 in., we need to calculate how many standard deviations higher than the mean 71 in. is. We subtract the mean (64 in.) from the height (71 in.) and divide by the standard deviation (3.5 in.).
(71 - 64) / 3.5 = 2
Since 71 in. is two standard deviations above the mean, we can refer to the z-table or use a calculator to find the percentage of data points falling above two standard deviations. Approximately 2.28% of the data falls above two standard deviations.
To find the number of sunflowers taller than 71 in., we multiply the total number of plants (3,000) by the percentage above two standard deviations.
3,000 * 0.0228 = 68.4
Therefore, approximately 68 sunflowers will be taller than 71 in.
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 in full sentence
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