A person's IQ (Intelligence Quotient) is supposed to be a measure of his or her "intelligence." The IQ test scores are normally distributed and are scaled to a mean of 100 and a standard deviation of 15. It is often said that a genius is someone with an IQ of 140 or more. What is the z-score for a 140 IQ? (Round your answer to one decimal place.) z = What percentage of the population scores as a genius? Round your answer as a percentage to one decimal place. %

Question

Mathematics

Clarissa Holmes

20 March, 21:28

A person's IQ (Intelligence Quotient) is supposed to be a measure of his or her "intelligence." The IQ test scores are normally distributed and are scaled to a mean of 100 and a standard deviation of 15. It is often said that a genius is someone with an IQ of 140 or more. What is the z-score for a 140 IQ? (Round your answer to one decimal place.) z = What percentage of the population scores as a genius? Round your answer as a percentage to one decimal place. %

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Jensen Mckee · Answer 1

2.7 and 99.6%

Step-by-step explanation:

In this question, we are asked to calculate the percentage of the population scores as a genius.

We proceed as follows;

z = (Mean - value) / standard deviation = (140 - 100) / 15 = 2.6667 = 2.7

From normal probability table, given that z = 2.67, the probability is 0.9962

This means that the required percentage is 99.6%