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. 108 to 124 A symmetric bell-shaped curve is plotted over a horizontal scale. Two vertical lines run from the scale to the curve at labeled coordinates 108 and 124, 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

Given,

= 100 , = 15

We convert this to standard normal as

P(X < x) = P( Z < x - / )

So,

P( 108 < X < 124) = P( X < 124) - P( X < 108)

= P( Z < 124 - 100 / 15) - P( Z < 108 - 100 / 15)

= P( Z < 1.6) - P (Z < 0.5333)

= 0.9452 - 0.7031 (Probability calculated from Z table)

= 0.2421