Question

The principal of a large local high school wants to know what proportion of her students are planning to attend college. Suppose that 72% of all students in her high school are planning to attend college. What is the probability that an SRS of size 200 will give a sample proportion between 66% and 78%?

0.939

0.061

0.099

0.815

Answer 1

Solution

Given that,

p = 0.72

1 - p = 1 - 0.72 = 0.28

n = 200

= p = 0.72

  [p ( 1 - p ) / n] = [(0.72 * 0.28 ) / 200 ] = 0.032

P( 0.66 < < 0.78 )

= P[(0.66 - 0.72) /0.032 < ( - ) / < (0.78 - 0.72) / 0.032]

= P(-1.875 < z < 1.875 )

= P(z < 1.875 ) - P(z < -1.875 )

Using z table,   

= 0.9696 - 0.0304

= 0.9392

Answer = 0.939