Question

a sample of 200 is drawn from a population with a proportion equal to .25. determine the probability of observing between 41 and 63 successes

Answer 1

Given that,

p = 0.25

q = 1 - p = 1 - 0.25 = 0.75

n = 200

Using binomial distribution,

= n * p = 200 * 0.25 = 50

= n * p * q = 200 * 0.25 * 0.75 = 6.1237

Using continuity correction ,

P(40.5 < x < 63.5) = P((40.5 - 50)/ 6.1237) < (x - ) / < (63.5 - 50) / 6.1237) )

= P(-1.55 < z < 2.20)

= P(z < 2.20) - P(z < -1.55)

= 0.9861 - 0.0606

= 09255

Probability = 0.9255