Question

A psychologist interested in right- handedness versus left-handedness. and in IQ scores collected the following data from a random sample of 2000 high school students. High IQ Right-handed. 190 Left-handed 10 Total 200Normal IQ:1710 Right-handed 90 Left-handed Total 1800.Total:1900 Right- handed. 100:Left- handed Total:2000.a) what is the probability that a Student from this group has a high IQ?b) what is the probability that a student has a high IQ given that. she is left- handed?c) Are high IQ and left-handed independent? Why or why not?

Answer 1

Explanation:

Given that a psychologist interested in right- handedness versus left-handedness. and in IQ scores collected the following data from a random sample of 2000 high school students.

High IQ Normal IQ

Right handed 190 1710 1900

Left handed 10 90 100

200 1800 2000

a) Using total probability theorem

The probability that a Student from this group has a high IQ

= Prob left handed and high iq + prob right handed and high iq

=
`(10+190)/(2000) =0.10`

b) the probability that a student has a high IQ given that. she is left- handed

= Prob for left handed and high iq/prob for left handed

=
`(10)/(100) =0.10`

c) Prob for high IQ = 0.10

Prob for being left handed = 100/2000 = 0.05

Prob for high iq and left handed = 0.10

Since prob for both is not product of individual prob we find that the two events high IQ and left-handed are not independent