Question

A recent survey at New York Univeristy found that 10% of students live in the dormitories. We've decided to select 100 NYU students for a study. What is the probability that the sample proportion of students living in the dormitories is greater than 0.07 (to 4 decimal places)?

Answer 1

Solution

Given that,

p = 0.10

1 - p = 1 - 0.10 = 0.90

n = 100

= p = 0.10

=  [p( 1 - p ) / n] = [(0.10 * 0.90) / 100 ] = 0.03

P( > 0.07 ) = 1 - P( < 0.07 )

= 1 - P(( - ) / < (0.07 - 0.10) / 0.03)

= 1 - P(z < -1.00)

Using z table

= 1 - 0.1587

= 0.8413