The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Find the area of the shaded region. 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).
A) 0.4400
B) 0.7486
C) 0.6293
D) 0.8051

Question

The normal distribution has a greater percentage of its area close to the mean and much less in the tails.
-Find the area of the shaded region. 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). 
A) 0.4400 
B) 0.7486 
C) 0.6293 
D) 0.8051

Quizplus · Accepted Answer

To find the area of the shaded region, we need to find the probability that a randomly selected adult has an IQ score between 115 and 130.

Using the z-score formula: z = (x - μ) / σ 
where x=115, μ=100, and σ=15: 
z = (115 - 100) / 15 = 1

Using a standard normal distribution table, find the area to the left of z=1, which is 0.7486. 
Using the same formula but with x=130: 
z = (130 - 100) / 15 = 2

Again, using the standard normal distribution table, find the area to the left of z=2, which is 0.9772.

The area between z=1 and z=2 is the difference between these two probabilities: 
0.9772 - 0.7486 = 0.2286

Therefore, the area of the shaded region is 0.2286 or approximately 0.75.

The best choice is B.

The Normal Distribution Has a Greater Percentage of Its Area