The heights of the adults in one town have a bell-shaped distribution with a mean of 67.5 inches and a standard deviation of 3.4 inches. Based on the empirical rule, what should you predict about the percentage of adults in the town whose heights are between 57.3 and 77.7 inches?

The heights of the adults in one town have a bellshaped distribution with a mean of 675 inches and a standard deviation of 34 inches Based on the empirical rule class=

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Answer:

The percentage is approximately 99.7%

Step-by-step explanation:

In order to understand this question you must understand the bell curve. (I would suggest googling a picture of the bell curve)

The mean of the bell curve is 67.5, meaning +1 standard deviation would be 70.9 (67.5+3.4). This would mean that 34% of the sample is between 67.5" and 70.9" (The bell curve % goes 34/14/2/.1 in that order)

When looking at the bell curve of this data, you would find that ±3 standard deviations gives you the range of 57.3" to 77.7". This would represent roughly (2+14+34+34+14+2)% of the sample. This excludes the .2% that are above or below 57.3" to 77.7". Therefore, the only answer that is close would be 99.7%