A question reads: "The weights of $910$ young deer tagged and weighed in a research study are normally distributed with a mean of $86$ pounds and a standard deviation of $2.5$ pounds."
Approximately how many deer weigh more than $91$ pounds?
Since $34.1$% fall within the first standard deviation and $13.6$% fall within the second standard deviation, then $2.3$% will be greater than two standard deviations. $2.3$% of $910$ equals $20.93$.
Possible multiple choice answers are $21$ or $23$. I picked $21$. The test guide says $23$. I assume this is a typo. Anyone think I went awry?
Best Answer
The answer key may be using the rougher guide ('empirical rule') that about $95\%$ of the area under a normal curve is within $2$ standard deviations of the mean. So about $2.5\%$ of the data is more than $2$ standard deviations above the mean. And $2.5\%$ of $910$ is $22.75$, close to their answer of $23$.
However, your answer is more accurate.