Question

Random samples of size n = 90 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(0.26 ≤ p̂ ≤ 0.34) =

Answer 1

Using normal approximation,

P( < p ) = P( Z < ( - p) / sqrt [ p ( 1 - p) / n ]

So,

P( 0.26 < < 0.34) = P( < 0.34) - P( < 0.26)

= P(Z < ( 0.34 - 0.30) / sqrt [ 0.30 (1 - 0.30) / 90] < p < P(Z < ( 0.26 - 0.30) / sqrt [ 0.30 (1 - 0.30) / 90]

= P(Z < 0.83) - P(Z < -0.83)

= 0.7967 - 0.2033 (From Z table)

= 0.5934