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. In 1-3 sentences
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 1-3 sentences
a) On the normal curve drawing, the mean of 64 in. is at the center, with one standard deviation to the left at 60.5 in. and to the right at 67.5 in., two standard deviations to the left at 57 in. and to the right at 71 in., and three standard deviations to the left at 53.5 in. and to the right at 74.5 in. These values were calculated by adding/subtracting the standard deviation (3.5 in.) from the mean.
b) To find the number of sunflowers taller than 71 in., first, we need to calculate how many standard deviations 71 in. is from the mean. (71-64)/3.5 = 2. Using the z-score table, we can find that approximately 2.28% of the sunflowers will be taller than 71 in., which is equivalent to 68.4 plants (2.28% of 3,000).