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The heights of German men are normally distributed with a mean of 71 inches and a standard deviation of 5.6 inches, According to the empirical rule, what percentage of German men are:(a) Over 65.4 inches tall?Answer: %(b) Between 59.8 and 82.2 inches tall?Answer: %(c) Under 76.6 inches tall?Answer: %

User Trond Nordheim
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1 Answer

22 votes
22 votes

Part A

According to the empirical rule 68% of the german men are between 65.4 and 76.6 inches tall (1 standard deviation). It means that half the remaining percentage is over 76.6 inches tall. We would have to add the percentage of those who are between 65.4 and 76.6 to the one that represents those who are over 76.6 inches tall.

Doing so, we have:

68% + 16% = 84%

The answer is 84%.

Part B

Using the empirical rule the interval falls within 2 standard deviations. Therefore, the percentage is 95%.

Part C

According to the empirical rule 68% of the german men are between 65.4 and 76.6 inches tall (1 standard deviation). It means that half the remaining percentage is under 65.4 inches tall. Therefore, 16% are under 65.4 inches tall.

We have to add 68% and 16 % to find the percentage of german men under 76.6 inches tall.

The answer of part C is 84%.

User Kostas Tsoleridis
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2.8k points
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