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Question 620100: (A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30.
(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30.
P(x=6) = 15C6*0.3^6*0.7^9 = binompdf(15,0.3,6) = 0.1472
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(B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation.
P(0<= x <=6) = binomcdf(15,0.3,6) = 0.8689
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(C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
mean = np = 15*0.3 = 4.5
std = sqrt(npq) = sqrt(4.5*0.7) = 1.7748
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P(x = 6) = P(5.5<= x <= 6.5)
z(5.5) = (5.5-4.5)/1.7748 = 0.5634
Z(6.5) = (6.5-4.5)/1.7748 = 1.1269
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Then approx P(x = 6) = P(0.5634< z < 1.1269) = 0.1567
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Cheers,
Stan H.
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