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
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
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