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. The graph shows 80 and 125

Answer 1

Solution :

Given that,

mean = = 100

standard deviation = = 15

P ( 80 < x < 125 )

P ( 80 -100 / 15) < ( x -  / ) < ( 125 - 100 / 15)

P ( - 20 / 15 < z < 25 / 15)

P (-1.33 < z < 1.67)

P ( z < 1.67 ) - P ( z < -1.33 )

Using z table

= 0.9525- 0.0918

= 0.8607

The area of the shaded region = 0.8607