Question from http://www.sgforums.com/forums/2297/topics/355089
A dancer performs a certain routine faultlessly 80% of the time. Using a suitable approximation, find the probability that in 160 such occasions, she will perform the routine faultlessly on at least 75% of the number of such occasions.
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Answer:
Y ~ B(160, 0.8)
Let X be the Normal Approximation to Binomial, i.e. X ~ N (128, 25.6)
75% of 160 = 120
Thus,
P(Y > 120) = P(X ≥ 120.5) by Normal Approximation
= 0.931 using Graphic Calculator
