Respuesta :
This is from https://www.jiskha.com/questions/1578462/a-the-average-height-of-sunflowers-in-a-field-is-64-inches-with-a-standard-deviation-of
Answer:
a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its
maximum value at x = 64.
Important points:
mean - 3 deviations: 64 - 3(3.5) = 64 - 10.5 = 53.5
mean - 2 deviations: 64 - 2(3.5) = 64 - 7 = 57
mean - 1 deviation: 64 - 3.5 = 60.5
mean: = 64
mean + 1 deviation: 64 + 3.5 = 67.5
mean + 2 deviations: 64 + 2(3.5) = 64 + 7 = 71
mean + 3 deviations: 64 + 3(3.5) = 64 + 10.5 = 74.5
b) If there are 3000 plants, approximately how many will be taller than 71"?
71" is 2 standard deviations above the mean. The region between two standard deviations below the mean and two standard deviations holds approximately 95% of the plants.
Therefore there will be approximately 5% of the plants divided equally between being taller than two standard
deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be
approximately 2.5% of the plants taller than 71": 0.025 x 3000 = 75 plants.
