a) To draw the normal curve, start by marking the mean height of 64 in. at the center of the horizontal axis. Then, mark one standard deviation above and below the mean at 67.5 in. and 60.5 in., two standard deviations above and below the mean at 71 in. and 58.5 in., and three standard deviations above and below the mean at 74.5 in. and 55.5 in. Draw the curve smoothly connecting these points to create a bell-shaped curve. Label each point with the corresponding heights.
b) To find out approximately how many plants will be taller than 71 in., we need to calculate the z-score for a height of 71 in. using the formula z = (x - μ) / σ, where x is the value (71), μ is the mean (64), and σ is the standard deviation (3.5).
z = (71 - 64) / 3.5 = 2
Looking at a standard normal distribution table, we find that the proportion of values above z = 2 is approximately 0.0228, which means about 2.28% of the plants will be taller than 71 in. Out of 3,000 plants, this would be approximately 68 plants.
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. short answer
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