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.

Question

kirbykirby · Answer

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|