Problem

Question 24 IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160, Convert Einsteins IQ score to a z-score. No rounding necessary, please type in the exact answer.

Solution

Step 1 :Given that the mean IQ score is 100 and the standard deviation is 16.

Step 2 :Albert Einstein reportedly had an IQ of 160.

Step 3 :The z-score is a measure of how many standard deviations an element is from the mean.

Step 4 :To calculate the z-score of a value, we subtract the mean from it and then divide by the standard deviation.

Step 5 :Subtract the mean IQ from Einstein's IQ: \(160 - 100 = 60\).

Step 6 :Divide the result by the standard deviation: \(\frac{60}{16} = 3.75\).

Step 7 :Final Answer: The z-score for Einstein's IQ is \(\boxed{3.75}\).

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