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.
106 124
The area of the shaded region is (Round to four decimal places as needed.)

Answer 1

Answer:

The area of the shaded region is 0.2898.

Step-by-step explanation:

Let X represent the IQ scores of adults.

It is provided that $X\sim N(100,15^{2})$.

Compute the probability of an adult having an IQ between 106 and 124 as follows:

$P(106<X<124)=P(\frac{106-100}{15}<\frac{X-\mu}{\sigma}<\frac{124-100}{15})$

                             $=P(0.40<Z<1.60)\\=P(Z<1.60)-P(Z<0.40)\\=0.94520-0.65542\\=0.28978\\\approx 0.2898$

*Use a z-table.

Thus, the area of the shaded region is 0.2898.