Question

Random samples of size n = 85 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 < 0.70) =

Answer 1

Solution

Given that,

p = 0.8

1 - p = 1 - 0.8 = 0.2

n = 85

= p = 0.8

=  [p ( 1 - p ) / n] =   [(0.8 * 0.2) / 85 ] = 0.0434

P( < 0.70)

= P[( - ) / < (0.70 - 0.8 ) / 0.0434 ]

= P(z < -2.30)

Using z table,

= 0.0107