Question

Adult IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical Rule to find the percentage of adults with scores between 55 and 145.

Answer 1

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Answer 2

\[z_{1}=\frac{x-\mu}{\sigma}=\frac{145-100}{15}=3\]\[\Phi(3)=0.9987\]So the proportion that lies in the interval 100-145 is 0.9987-0.5=0.4987. By inspection, you can see that the amount of people that lie in the interval 55-100 will be the same as the people in 100-145 (because the normal distribution is symmetrical. So the answer is 2x0.4987=0.9974=99.74%.