Answer :
Therefore, the height range that encompasses 99.7% of adolescent women is roughly between 55.9 and 68.1 inches.
What can you infer from standard deviation?
It reveals the average deviation of each number from the norm. When it comes to normally distributed, a large standard deviation denotes that values are typically out of the mean, whereas a smaller standard deviation denotes that values are grouped closely around the mean.
The 68-95-99.7 rule is a way to remember the percentage of data that falls within certain numbers of standard deviations from the mean in a normal distribution. Specifically:
- About 68% of the data falls within 1 standard deviation of the mean
- About 95% of the data falls within 2 standard deviations of the mean
- About 99.7% of the data falls within 3 standard deviations of the mean
Using this rule, we can answer the following questions:
- What is the range of heights that includes about 68% of young women?
About 68% of young women have heights within 1 standard deviation of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 1 standard deviation from the mean:
64 inches ± 2.7 inches
So the range of heights that includes about 68% of young women is approximately 61.3 inches to 66.7 inches.
2. What is the range of heights that includes about 95% of young women?
About 95% of young women have heights within 2 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 2 standard deviations from the mean:
64 inches ± 2(2.7 inches)
So the range of heights that includes about 95% of young women is approximately 58.6 inches to 69.4 inches.
3. What is the range of heights that includes about 99.7% of young women?
About 99.7% of young women have heights within 3 standard deviations of the mean. Therefore, we can find the range of heights that includes this percentage by adding and subtracting 3 standard deviations from the mean:
64 inches ± 3(2.7 inches)
So the range of heights that includes about 99.7% of young women is approximately 55.9 inches to 68.1 inches.
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