Question

at a certain university, 50% of all entering freshmen planned to major in a STEM discipline. a sample of 36 freshmen is selected. what is the probability that the proportion of freshmen in the sample is between 0.484 and 0.580? Round to four decimal places

Answer 1

Solution

Given that,

p = 0.50

1 - p = 1 - 0.50 = 0.50

n = 36

= p = 0.50

=  [p ( 1 - p ) / n] = [(0.50 * 0.50) / 36 ] = 0.0833

P( 0.484 < < 0.580 )

= P[(0.484 - 0.50) /0.0833 < ( - ) / < (0.580 - 0.50) / 0.0833 ]

= P(-0.19 < z < 0.96)

= P(z < 0.96) - P(z < -0.19)

Using z table,   

= 0.8315 - 0.4247

= 0.4068