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Here is the problem: A score of 3.5 comes from a distribution with mean 3.0 and standard deviation 0.4. Find its z-score.

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Z-score from x, mean and SD.

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Subtract the mean from the value.

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Divide by the standard deviation.

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Look up the area to the left (percentile).

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So the answer is z equals 1.25 (percentile approximately 89.44 percent).

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3.5 lies 1.25 standard deviations above the mean; about 89.44 percent of a normal population lies below it.

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Reverse: μ plus zσ equals 3 plus (1.25)(0.4) equals 3.5.