+2441 A) This drawing was electronically generated, but it represents the situation well; it contains the normal distribution with the correct mean and standard distribution:
The purpose of the title of any graph is to communicate the overall message concisely. This title does just that. It explains to the viewer in few words what to expect. The horizontal axis explains the full meaning of the labeled data points; they represent the height of the sunflower in inches. It is OK that the title and the axis label overlap. This will often be the case when constructing simple diagrams like this one. Be sure to include the unit label (centimeters, seconds, kelvin, ampere, mole, etc).
B) The empirical rule (sometimes referred to as the 68-95-99.7% rule) will be extremely key here. Notice how the previous graph shows that 71 is two standard deviations away from the mean, 64. We know that, for a standard distribution, anything to the left of the mean, 64, represents 50% of the data. The empirical rule tells us that 64-67.5 represents 34% of the data, and 67.5-71 represents 13.5% of the data. Therefore, \(50+34+13.5=97.5\) percent of the data is less than this. Subtracting this from 100 would yield 2.5% of the flowers are taller than 71 inches. Since you know that there are 3000 plants, multiply that by the percentage of flowers, 2.5%. \(3000*2.5\%=75\text{ sunflowers} \)
+2441 A) This drawing was electronically generated, but it represents the situation well; it contains the normal distribution with the correct mean and standard distribution:
The purpose of the title of any graph is to communicate the overall message concisely. This title does just that. It explains to the viewer in few words what to expect. The horizontal axis explains the full meaning of the labeled data points; they represent the height of the sunflower in inches. It is OK that the title and the axis label overlap. This will often be the case when constructing simple diagrams like this one. Be sure to include the unit label (centimeters, seconds, kelvin, ampere, mole, etc).
B) The empirical rule (sometimes referred to as the 68-95-99.7% rule) will be extremely key here. Notice how the previous graph shows that 71 is two standard deviations away from the mean, 64. We know that, for a standard distribution, anything to the left of the mean, 64, represents 50% of the data. The empirical rule tells us that 64-67.5 represents 34% of the data, and 67.5-71 represents 13.5% of the data. Therefore, \(50+34+13.5=97.5\) percent of the data is less than this. Subtracting this from 100 would yield 2.5% of the flowers are taller than 71 inches. Since you know that there are 3000 plants, multiply that by the percentage of flowers, 2.5%. \(3000*2.5\%=75\text{ sunflowers} \)
