SOLUTION: 3. Assume a binomial probability distribution has p = .60 and n = 200.
a. What are the mean and standard deviation?
b. Is this situation one in which binomial probabilities can b
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Question 861562: 3. Assume a binomial probability distribution has p = .60 and n = 200.
a. What are the mean and standard deviation?
b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution?
c. What is the probability of 100 to 110 successes?
d. What is the probability of 130 or more successes?
e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume a binomial probability distribution has p = .60 and n = 200.
a. What are the mean and standard deviation?
mean = np = 200*0.6 = 120
std: = sqrt(npq) = sqrt(120*0.4) = sqrt(48) = 4sqrt(3)
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b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution?
Yes:: Both np and qp > 5
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c. What is the probability of 100 to 110 successes?
Find P(99.5 <= x <= 110.5)
z(99.5) = (99.5-120)/sqrt(48) = -2.95
z(110.5) = (110.5-120)/sqrt(48) = -1.37
P(99.5<= x <=110.5) = P(-2.95<= z <=-1.37) = 0.0838
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Use the same procedure on the next problem.
d. What is the probability of 130 or more successes?
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e. What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
Check your textbook to discuss these advantages.
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Cheers,
Stan H.
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