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Answer :
The question is asking about calculations involving the normal distribution of male adult heights. It is answered by using the properties of a normal distribution, including the rules of 68-95-99.7 and the z-score formula. Z = (X - μ)/σ where X is the data point, μ is the mean and σ is the standard deviation.
The question is about the distribution of the heights of adult males which follows a normal distribution, often known as a bell curve, with a mean of 174 cm and a standard deviation of 7 cm. In such distributions, approximately 68% of the data falls within one standard deviation of the mean, 95% fall within two standard deviations and 99.7% fall within three standard deviations.
With this in mind, for example to calculate the percentage of heights greater than 174 cm, given that the mean height itself is 174 cm, it would be 50% as half of the data falls above the mean. To find the percentage of heights less than 181 cm, you would use the z-score formula to convert the height into a standard score, which can be looked up in a z-table to give percentages. The z-score formula Z = (X - μ)/σ, where X is the data point, μ is the mean and σ is the standard deviation. In this case, the calculation would be Z = (181 - 174) / 7 = 1. This would mean approximately 84% since in a standard normal distribution, 84% of the data falls below one standard deviation above the mean.
Similar calculations can be done for the rest of the heights given in the question using the same method. Remember, on a normal distribution, the mean splits the distribution directly in half, and the percentage of data that falls within a certain range of standard deviations from the mean can be determined using the rules of 68-95-99.7, or by converting to a z-score and looking up the associated percentage in a z-table.
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The probable question may be:
Heights of Males. For Exercises 25-36, sketch the normal distribution of heights of adult males, which has a mean of 174 cm and a standard deviation of 7 cm, then shade the de- scribed area. Use Table A-1 to find the indicated quantities. 25. The percentage of heights greater than 174 cm pm bpm behavior, eye con- ormally d devia- Study of phrenic ol. 144, ntity 26. The percentage of heights less than 181 cm 27. The percentage of heights greater than 181 cm 28. The percentage of heights greater than 167 cm 29. The percentage of heights less than 160 cm 30. The percentage of heights less than 200 cm 31. The percentage of heights less than 146 cm of the 32. The percentage of heights greater than 180 cnm 33. The percentage of heights between 167 cm and 181 cm of the 34. The percentage of heights between 160 cm and 188 cm 35. The percentage of heights between 180 cm and 200 cm s and 36. The percentage of heights between 150 cm and 170 cm
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