Question

Random samples of size n = 90 were selected from a binomial population with p = 0.8. Use the normal distribution to approximate the following probability. (Round your answer to four decimal places.)

P(p̂ > 0.78) =

Answer 1

Solution:

Given that,

n = 90

= 0.8

1 - = 1 - 0.8 = 0.2

=   = 0.8

= ( 1 - ) / n

=   0.80 * 0.20 / 90

= 0.0422

= 0.0422

p (   > 0.78 )

= 1 -  p (   < 0.78 )

= 1 - p ( -    / ) < ( 0.78 - 0.8 / 0.0422 )

= 1 - p ( z < -0.02 / 0.0422 )

= 1 - p ( z < -0.47 )

Using z table

= 1 - 0.3192

= 0.6808

Probability = 0.6808