Question

A local statistician is interested in the proportion of high school students that drink coffee. Suppose that 20% of all high school students drink coffee. A sample of 75 high school students are asked if they drink coffee.

What is the probability that out of these 75 people, 14 or more drink coffee?

Answer 1

Solution

Given that,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 75

= p = 0.20

=  [p( 1 - p ) / n] = [(0.20 * 0.80 ) / 75 ] = 0.0462

sample proportion = = x / n = 14 / 75 = 0.19

P(    0.19) = 1 - P( 0.19)

= 1 - P(( - ) /    (0.19 - 0.20) / 0.0462)

= 1 - P(z -0.22)

Using z table

= 1 - 0.4129

= 0.5871