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?

Step-by-step 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                            17101900

Left handed           10                               90100

                       200                            18002000

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

=

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

=

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

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50