Question 405932: Answer the following:
(A) Find the binomial probability P(x = 5), where n = 12 and p = 0.60.
(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 5) 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 = 5), where n = 12 and p = 0.60.
Ans: 12C5(0.6)^5*(0.4)^7 = 0.1009
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(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
Ans: 12C0(0.6)^0*0.4^12+12C1(0.6)(0.4)^11+...+12C5(0.6)^5*(0.4)^7
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(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A?
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Find the z-values of 4.5 and 5.5
Find the probability z is between those two z-values.
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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*0.6 = 7.2
sigma = sqrt(npq) = sqrt(7.2*0.4)
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Cheers,
Stan H.
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