Question

At a certain college 50% of all students take advantage of free tutoring services a sample of 36 students is selected. What is the probability that the proportion of students who take advantage of free tutoring services in the sample is between 0.482 and 0.580

Answer 1

Solution :

Given that,

p = 0.50

q = 1 - p =1 -0.50 =0.50

n = 36

= p =0.50

=  [p ( 1 - p ) / n] = [(0.50*0.50) /36 ] = 0.083333333

= P( 0.482<< 0.580)= P[(0.482 -0.50) / 0.083333333< ( - ) / < (0.580 -0.50) / 0.083333333]

= P( -0.216< z <0.960 )

= P(z <0.960 ) - P(z < -0.216)

Using z table

=0.8315 -0.4145

=0.4170

probability= 0.4170