• anonymous
Weights of male mountain lions follow the normal distribution with a median of 150 pounds and an interquartile range of 8.2 pounds. Find the 75th percentile of the weights.
Collaborative Statistics
  • Stacey Warren - Expert
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  • schrodinger
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  • kirbykirby
In a normal distribution, the median = mean. Also, The mean = 50th percentile ("Q2") The interquartile range = Q3 - Q1 = 75th percentile - 25th percentile. Now, since the normal distribution is symmetric, half your data is below the mean, and half is above the mean. So, you proportionately find 8.2/2 = 4.1 pounds being Q3 - Q2 , and Q2 - Q1 Schematically: |dw:1397373422765:dw|
  • kirbykirby
Thus I hope you can see that Q3, the 75th percentile, is 150+4.1 = 154.1
  • kirbykirby
Maybe this picture is more clear:

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