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. 85 110

Answer 1

Solution:

Given, the Normal distribution with,

   = 100

= 15

P(85 < X < 110)

=  P(X < 110) - P(X < 85)

=  P[(X - )/ <  (110- 100)/15] -   P[(X - )/ <  (85- 100)/15]

= P[Z < 0.67] - P[Z < -1.00]

= 0.7486 - 0.1587..Use z table

= 0.5899