Answer to Question #106096 in Statistics and Probability for stephanie martin

Question

The mean score on a creativity test is 20 and the standard deviation is 5. The distribution is normal. Using the percentage approximations for the normal curve, how many people would attain a score between 15 and 25?

Answer 1

Let X be the random variable denoting the score of a person in the creativity test

$P(15<X<25) = P(-5<X-20<5)$

$P(-1<\frac{X-20}{5}<1) = \Phi(1) - \Phi(-1)$

$P(15<X<25) = 2\Phi(1) - 1 \approx 1.682-1 = 0.682$

Therefore, 68.2% people will score between 15 and 25 in the creativity test.