Question

At a certain university, 50% of all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.499 and 0.580? Write only a number as your answer. Round to 4 decimal places (for example 0.3748). Do not write as a percentage.

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( 0.499 << 0.580)= P[(0.499 -0.50) / 0.0833< ( - ) / < (0.580-0.50) /0.0833 ]

= P(-0.01 < z <0.96 )

= P(z <0.96 ) - P(z < -0.01)

Using z table

=0.8315-0.496

=0.3355

probability= 0.3355