Question 493497: A) Find the binomial probability P(x = 6), where n = 15 and p = 0.70.
(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 = 0.70.
P(x=6) = 15C6(0.7)^6*(0.3)^9 = 0.0116
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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) = (0.3)^15 + 15C1(0.7)(0.3)^14+...+15C6(0.7)^6(0.3)^9
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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.
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mean = u = np = 15*0.7 = 10.5
std = s = sqrt(npq) = sqrt(15*0.7*0.3) = 1.7748
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Using normal approximation:
P(x = 6) = P(5.5 < x < 6.5)
Find the z values 5.5 and of 6.5
Find the probability of z being between those z-values.
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Cheers,
Stan H.
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