Question

Random samples of size n = 80 were selected from a binomial population with p = 0.3. Use the normal distribution to approximate the following probability. (Round your answer to four decimal places.)

P(p̂ > 0.28) =

Answer 1

Solution

Given that,

p = 0.3

1 - p = 1 - 0.3 = 0.7

n = 80

= p = 0.3

=  [p( 1 - p ) / n] = [(0.3 * 0.7) / 80 ] = 0.0512

P( > 0.28) = 1 - P( < 0.28 )

= 1 - P(( - ) / < (0.28 - 0.3) / 0.0512)

= 1 - P(z < -0.39)

Using z table

= 1 - 0.3483

= 0.6517