Question 1075970: Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
n=58, p=0.3, and X=24
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
n=58, p=0.3, and X=24
p*n = 0.3*58 > 5
q*n = 0.7*58 > 5
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P(x = 24) = P(23.5 < x < 24.5)
np = 0.3*58 = 17.4
sqrt(npq) = sqrt(17.4*0.7) = 3.49
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z(23.5) = (23.5-17.4)/3.49 = 1.748
z(24.5) = (24.5-17.4)/3.49 = 2.034
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P(x = 24) = P(1.748< z < 2.034) = 0.0193 (normal approximation)
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P(x = 24) = 58C24(0.3^24)(0.7^34) = 0.0196
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Cheers,
Stan H.
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