Question

A large company employs workers whose IQs are distributed normally with mean 110 and standard deviation 12.5. Management uses this information to assign employees to projects that will be​ challenging, but not too challenging. What percent of employees would have IQs between 100 and 130​?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 110

standard deviation = $\sigma$ = 12.5

P( 100 < x < 130) = P[(100 - 110) / 12.5) < (x - $\mu$ ) /$\sigma$  < (130 - 110) / 12.5) ]

= P( - 0.8 < z < 1.6 )

= P(z < 1.6) - P(z < - 0.8 )

Using z table,

= 0.9452 - 0.2119

= 0.7333

73.33%