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If a normal distribution has and , what is the 91st percentile of the distribution?

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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.

User CJBrew
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