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. Shaded area is 108 to 128. The area of the shaded region is ____?

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 15

P(108 < x < 128) = P[(108 - 100)/ 15) < (x - ) /  < (128 - 100) / 15) ]

= P(0.5333 < z < 1.8667)

= P(z < 1.8667) - P(z < 0.5333)

= 0.969 - 0.7031

= 0.2659

The area of the shaded region is 0.2659