Question

12. Suppose that at a certain university, 65% of students live on campus. A professor performs a poll on her Statistics class of 120 students. What is the probability that the proportion of students in her class who live on campus will be between 65 and 70%?

Answer 1

Solution

Given that,

p = 0.65

1 - p = 1 - 0.65 = 0.35

n = 120

= p = 0.65

=  [p ( 1 - p ) / n] = [(0.65 * 0.35) / 120 ] = 0.0435

P( 0.65 <   < 0.70 )

= P[(0.65 - 0.65) /0.0435 < ( - ) / < (0.70 - 0.65) / 0.0435 ]

= P(0 < z < 1.15)

= P(z < 1.15) - P(z < 0)

Using z table,   

= 0.8749 - 0.5

= 0.3749