Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15. Determine the percentage of the population that would obtain a coefficient between 95 and 110.

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Answer to a math question Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15. Determine the percentage of the population that would obtain a coefficient between 95 and 110.

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\text{1. Convert the raw scores to the standard normal variable Z:}

Z = \frac{X - \mu}{\sigma}

\text{For X = 95:}

Z = \frac{95 - 100}{15} = -\frac{1}{3}

\text{For X = 110:}

Z = \frac{110 - 100}{15} = \frac{2}{3}

\text{2. Find the probability for these Z values using the standard normal distribution table:}

P(Z

\text{3. Compute the difference to find the percentage of the population within this score range:}

P(-\frac{1}{3}

\text{Therefore, the percentage of the population that would obtain a coefficient between 95 and 110 is 37.81\%}

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