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. Click to view page 1 of the table. Click to view page 2 of the table. 70 115 The area of the shaded region is (Round to four decimal places as needed.)

Answer 1

Let , $X\to N(\mu=100,\sigma=15)$

Now ,

70 – 100 P(70< X < 115) = P(- X- 115 – 100 15 15 0

$=P(-2.00<Z<1.00)=P(Z<1.00)-P(Z<-2.00)$

$=\Phi(1.00)-\Phi(-2.00)=\Phi(1.00)-[1-\Phi(2.00)]$

$=0.8413-1+0.9772=0.8185$ ; From standard normal distribution table

Therefore , the area of the shaded region is 0.8185