A national study found that 44 of college students engage in

A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). A professor surveyed a random sample of 244 students at his college.

What is the probability that less than 96 of them admitted to binge drinking in the past week?

Solution

A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). A professor surveyed a random sample of 244 students at his college.

What is the probability that less than 96 of them admitted to binge drinking in the past week?

p=0.44

n=244

Expectation = np = 107.36

Variance = np(1 - p) = 60.1216

Standard deviation = 7.7538

Normal distribution is used to approximate binomial

We take p( x < 96) =P( x 95.5) ( with correction)

Z value for 95.5, z = (95.5-107.36)/7.7538 = -1.53

P( x 95.5)

= P(z < -1.53)

= 0.063