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Suppose X has a normal distribution with mean 115 and variance 25. Find the 67th percentile...

Suppose X has a normal distribution with mean 115 and variance 25. Find the 67th percentile of the distribution of X.

Math   Statistics-And-Probability   
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Answer #1

Given that the X has a normal distribution with mean = 115 and variance = 25, hence the standard deviation is . To find the 67th percentile of the distribution of X we need to find the Z score at 67th percentile which is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.67), thus the Z is computed as 0.44

Now based on the Z -score formula the 67th percentile is computed as:

Thus the 67th percentile of the distribution of X is 117.2

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