Question 488543: (A) Find the binomial probability P(x = 4), where n = 12 and p = 0.70.
(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 4) 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 = 4), where n = 12 and p = 0.70.
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P(x = 4) = 12C4*(0.7)^4*(0.6)^8
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(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.
P(0<= x <=4) = normalcdf(12,0.7,4)
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(C) How would you find the normal approximation to the binomial probability P(x = 4) 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.
u = np = 12*0.7 = 8.4
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std = sqrt(npq) = sqrt(8.4*0.6) = 2.245
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P(x = 4) in binomial
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- P(3.5 < x < 4.5) in normal
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Find the z-value of 3.5 and of 4.5
Find the probability z is between those two z-values.
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Cheers,
Stan H.
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