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Based on a sample of 450 students, we found the average height is 165cm, with a...

Based on a sample of 450 students, we found the average height is 165cm, with a standard deviation of 6cm. a) Approximately how many percent of students are between 147 to 183cm? b) Assuming the histogram of height follows the normal distribution, approximately how many students have a height between 147 to 159cm? c) Assuming the histogram of height has a right skewed distribution, calculate the range of the height that will cover at least 71% of the students?

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Answer #1

Since we are given with the mean and standard deviation of the sample, we have a clear indication to use the normal distribution here. We can also use the Excel commands to solve this problem. =NORMDIST(X, Mean, Standard Deviation, TRUE) is the command to solve this problem. To get the value between the intervals, subtract the p-value obtained from bigger value to the smaller value using the NORMDIST function.

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