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680
8%
1/12
840
0%
0/12
950
17%
2/12
975
75%
9/12
997
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This study analyzes a population that follows a normal distribution with a mean of 200 and a standard deviation of 50. Since 95% of the population falls within 2 standard deviations (corresponding to a cholesterol less than 300 as the +2 standard deviation mark) and 5% of the population is outside of 2 standard deviations (2.5% on both sides), this means that 97.5% of the population has a cholesterol < 300 mg/dL (.975*1000 = 975). In a normal distribution, +/- 1 standard deviation captures 68% of the population, +/- 2 standard deviations captures 95% of the population, and +/- 3 standard deviations captures 99.7% of the population. Standard deviation is a value that suggests, on average, how different is a random data point from the mean. These standard deviations and percentages should be memorized and can be used to assess a population. The number of individuals that are less than a certain percentile involves knowing the area under the normal distribution curve. This can be calculated by % under the curve (which can be determined by knowing the aforementioned standard deviations and areas under the curve) times the total population. Incorrect Answers: Answer 1: 680 people fall within +/- 1 standard deviation of the mean. Since 68% of the population is within +/- 1 standard deviation, 68%*1000 = 680. Answer 2: 840 is the number of people that have a cholesterol < 250 as this is + 1 standard deviation from the mean. This would mean that 16% of the population has a cholesterol value greater than this (as 16% is outside the +1 STD on the left), and 84% have a cholesterol value less than this. For this calculation, 84%*1000 = 840. Answer 3: 950 people fall within 2 standard deviations of the mean. This value can be calculated by 95%*1000 = 950. Answer 5: 997 people fall within 3 standard deviations of the mean. This can be calculated by 99.7%*1000 = 997. Bullet Summary: In a normal distribution, +/- 1 standard deviation captures 68% of the population, +/- 2 standard deviations captures 95% of the population, and +/- 3 standard deviations captures 99.7% of the population.
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