Question

A psychologist finds that the intelligence quotients of a group of patients are normally distributed, with a mean of 104 and a standard deviation of 16. Find the percent of the patients with the following IQs.

(a) above 116
%

(b) between 92 and 122

Answer 1

Solution :

Given that ,

mean = = 104

standard deviation = = 16

(a)

P(x > 116) = 1 - P(x < 116)

= 1 - P[(x - ) / < (116 - 104) / 16)

= 1 - P(z < 0.75)

= 1 - 0.7734

= 0.2266

Percent = 22.66%

(b)

P(92 < x < 122) = P[(92 - 104)/ 16) < (x - ) /  < (122 - 104) / 16) ]

= P(-0.75 < z < 1.125)

= P(z < 1.125) - P(z < -0.75)

= 0.8697 - 0.2266

= 0.6431

Percent = 64.31%