The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the probability that a randomly selected adult has an IQ between 90 and 120
(somewhere in the range of normal to bright normal).
A) 0.6227
B) 0.6568
C) 0.6014
D) 0.6977

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected adult has an IQ between 90 and 120, we need to find the area under the normal distribution curve between these two values. We can do this by standardizing the values using the formula: z = (x - μ) / σ, where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For x = 90: 
z = (90 - 100) / 15 = -0.67

For x = 120: 
z = (120 - 100) / 15 = 1.33

Using a standard normal distribution table or calculator, we can find the probability of a z-score between -0.67 and 1.33 to be approximately 0.6568. Therefore, the answer is B.

The Normal Distribution Has a Greater Percentage of Its Area