Question

some IQtest are standardized to a normal model, mean is 100 and sd is 16

a)what percent of people should have IQ scores above 114?

b) what percent of people should have IQ scores between 65 and 84

c) what percent of people should have IQ scores above 132 or below 68

d) in what interval of iq scores would expect to be central 95% of iq scores to be found

Answer 1

Solution :

Given that ,

mean = $\mu$ = 100

standard deviation = $\sigma$ = 16

(a)

P(x > 114) = 1 - P(x < 114)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (114 - 100) / 16]

= 1 - P(z < 0.875)

= 0.1908

= 19.08%

(b)

P(65 < x < 84) = P[(65 - 100)/ 16) < (x - $\mu$ ) /$\sigma$  < (84 - 100) / 16) ]

= P(-2.1875 < z < -1)

= P(z < -1) - P(z < -2.1875)

= 0.1587 - 0.0144

= 0.1443

14.43%

(c)

= 1 - P(68 < x < 132) = P[(68 - 100)/ 16) < (x - $\mu$ ) /$\sigma$  < (132 - 100) / 16) ]

= 1 - P(-2 < z < 2)

= 0.0455

4.55%

(d)

z = -1.96 and z = +1.96

Using z-score formula,

x = z * $\sigma$ + $\mu$

= -1.96 * 16 + 100 = 68.64

= 1.96 * 16 + 100 = 131.36

Interval : 68.64 to 131.36