Question

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

Select one:

a. 0.0336

b. 0.9664

c. 0.9328

d. 0.4664

Answer 1

Solution:

Given that,

n = 80

= 40% = 0.40

1 - = 1 - 0.40= 0.60

So,

a ) =   = 0.40

=   ( 1 - ) / n

=   0.40 * 0.60 / 80

= 0.05477

= 0.05477

p (   > 0.30 )

= 1 -  p (   < 0.30 )

= 1 - p ( -    / ) < ( 0.30 - 0.40 / 0.05477 )

= 1 - p ( z < - 0.10 / 0.05477)

= 1 - p ( z < - 1.83 )

Using z table

= 1 - 0.0336

= 0.9664

Probability = 0.9664

Option b ) is correct.