Question

A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that the belief is correct. A random sample of 130 stockholders is take. What is the probability that the sample proportion of those stockholders that find the terms attractive will be between .18 and .23?

Answer 1

Solution

Given that,

p = 0.20

1 - p = 1-0.20=0.80

n = 130

= p =0.20

=  [p ( 1 - p ) / n] = [(0.20*0.80) /130 ] = 0.03508

= P( 0.18<<0.23 )= P[(0.18-0.20) /0.03508 < ( - ) / < (0.23-0.20) / 0.03508]

= P( -0.57< z <0.86 )

= P(z < 0.86) - P(z <-0.57 )

Using z table

=0.8051-0.2843

=0.5208

probability= 0.5208