Question

3. In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.

1. What is the sampling distribution of

2. What is the probability that the sample proportion is between 0.30 and 0.55(Hint: first draw the normal curve to identify the area)

Answer 1

Solution

Given that,

p = 0.40

1 - p = 1-0.40=0.60

n = 80

= p =0.40

=  [p ( 1 - p ) / n] = [(0.40*0.60) /80 ] = 0.05

= P[(0.30-0.40) /0.05 < ( - ) / < (0.55-0.40) / 0.05]

= P( -2< z <363 )

= P(z <3 ) - P(z < -2)

Using z table,   

= 0.9987-0.0228

=0.9759