Question 382254: I am not understanding this
1). x has a normal distribution with a mean of 80.0 and a standard deviation of 3.5 Find the following probabilities:
A). P(x < 75.0)
B). P(75.0 < x < 85.0)
C). P(x > 89.0)
2). A).Find the binomial probability P(x = 5), where n = 14 and p = 0.50
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! 1). x has a normal distribution with a mean of 80.0 and a standard deviation of 3.5 Find the following probabilities:
A). P(x < 75.0) = 0.0766
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B). P(75.0 < x < 85.0) = 0.8469
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C). P(x > 89.0) = 0.0051
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2).
A).Find the binomial probability P(x = 5), where n = 14 and p = 0.50
P(x=5) = 14C5(0.5)^5*0.5^9 = 0.1222
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B).Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
Ans: P(0<= x <=5) = P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5) = 0.2120
Comment: Use the pattern used in "A" on each of the terms to get the answer.
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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.
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u = np = 14*0.5 = 7
std = sqrt(npq) = sqrt(7*0.5) = sqrt(3.5)= 1.8708
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P(x=5) = P(4.5< x <5.5) = normalcdf(4.5,5.5,7,1.8708) = 0.1206
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Cheers,
Stan H.
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