Question 672683: Could someone please help me to understand this problem. I am not sure how to go about even trying to do it. Thanks in advance it is very much appreciated.
Answer the following:
(A) Find the binomial probability P(x = 5), where n = 14 and p = 0.30.
(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 = 14 and p = 0.30.
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P(x = 5) = 14C5*0.3^5*0.7^9 = binompdf(14,0.3,5) = 0.1963
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(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
P(0<= x <=5) = binomcdf(14,0.3,5) = 0.1963
I used a TI-84+
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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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The noral approx calls for P(4.5<= x <=5.5)
u = np = 14*0.3 = 4.2
std = sqrt(npq) = sqrt(4.2*0.7) = 1.71
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z(4.5) = (4.5-4.2)/1.71 = 0.1754
z(5.5) = (5.5-4.2)/1.71 = 0.7502
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P(4..5<= x <=5.5) = P(0.1754<= z <=0.7502) = 0.2038
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Cheers,
Stan H.
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