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%?
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
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