Question

Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 104 130 A symmetric bell-shaped curve is plotted over a horizontal scale. Two vertical lines run from the scale to the curve at labeled coordinates 104 and 130, which are both to the right of the curve’s center and peak. The area under the curve between the vertical lines is shaded. The area of the shaded region is _____. ​(Round to four decimal places as​ needed.)

Answer 1

Solution:

We are given that IQ scores are normally distributed.

Mean = 100

SD = 15

We have to find P(104<X<130)

P(104<X<130) = P(X<130) – P(X<104)

First find P(X<130)

Z = (X – mean) / SD

Z = (130 – 100)/15

Z = 30/15

Z = 2

P(Z<2) = P(X<130) = 0.97725

(by using z-table)

Now, find P(X<104)

Z = (X – mean) / SD

Z = (104 – 100)/15

Z = 4/15

Z = 0.266667

P(Z< 0.266667) = P(X<104) = 0.605137

(by using z-table)

P(104<X<130) = P(X<130) – P(X<104)

P(104<X<130) = 0.97725 – 0.605137

P(104<X<130) = 0.372113

Required probability = 0.3721

The area of the shaded region is 0.3721.