Final answer:
To find the 91st percentile of a normal distribution, we can use the formula z = (x - μ) / σ, where z is the z-score and x is the value we want to find. Plugging in the given values, we can solve for x to find the 91st percentile.
Step-by-step explanation:
To find the 91st percentile of a normal distribution, we need to find the z-score that corresponds to this percentile and then use it to find the corresponding value. The formula for finding the z-score is:
z = (x - μ) / σ
Where x is the value we want to find, μ is the mean, and σ is the standard deviation. In this case, the mean is 2008.5 and the standard deviation is 72.56. Plugging in these values, we can solve for x:
(x - 2008.5) / 72.56 = invNorm(0.91,0,1)
Solving for x gives us:
x ≈ 2140.29
Therefore, the 91st percentile of the distribution is approximately 2140.29.