Question

Below, n is the sample size, p is the population proportion, and p is the sample proportion. Use the Central Limit Theorem and the Cumulative normal distribution table

yo find the probability. Round your answer to at least four decimal places. n=200 p=0.10

P(0.12 < p < 0.16)=?

Answer 1

Solution

Given that,

p = 0.10

1 - p = 1 - 0.10 = 0.90

n = 200

= p = 0.10

  [p ( 1 - p ) / n] = [(0.10 * 0.90) / 200 ] = 0.0212

P( 0.12 < < 0.16 )

= P[(0.12 - 0.10 ) / 0.0212 < ( - ) / < (0.16 - 0.10) / 0.0212 ]

= P( 0.94 < z < 2.83)

= P(z < 2.83) - P(z < 0.94)

Using z table,   

= 0.9977 - 0.8264

= 0.1713