The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). The shaded area under the curve is 0.5675.
A) 97.5
B) 129.6
C) 102.6
D) 110.7

Question

The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).  The shaded area under the curve is 0.5675.
A) 97.5 
B) 129.6 
C) 102.6 
D) 110.7

Quizplus · Accepted Answer

Using a standard normal distribution table, we can find the z-score that corresponds to the shaded area of 0.5675. The closest value to 0.5675 in the table is 0.57, which corresponds to a z-score of 0.18. We can then use the formula z = (x - mu) / sigma and plug in the given values to solve for x, the IQ score we are trying to find:

0.18 = (x - 100) / 15
2.7 = x - 100
x = 102.7

Rounding to one decimal place, we get an IQ score of 102.6, which corresponds to choice C.

The Normal Distribution Has a Greater Percentage of Its Area