High School

IQ is normally distributed with a mean of 100 and a standard deviation of 16. A local school is considering what its minimum IQ score should be for admission.

What should the minimum IQ score be so that 90% of all students in the area can qualify for admission?

Round your answer to the nearest whole number.

Answer :

Final answer:

The minimum IQ score for admission should be approximately 121.

Explanation:

To determine the minimum IQ score for admission, we need to find the IQ score that corresponds to the 90th percentile. Since IQ is normally distributed with a mean of 100 and a standard deviation of 16, we can use the standard normal distribution table or a calculator to find the z-score that corresponds to the 90th percentile, which is approximately 1.28. Using the formula z = (x - μ) / σ, we can rearrange it to x = z * σ + μ and substitute the values. Therefore, the minimum IQ score for admission should be approximately 121.

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