SOLUTION: Their is a 80 % chance it will rain on any given day in Seattle what is the probability that of 118 random selected days there will be rain on at most 90 of them

Question 1105650: Their is a 80 % chance it will rain on any given day in Seattle what is the probability that of 118 random selected days there will be rain on at most 90 of them
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
118 * 0.80 = 94.4 is the mean of the sample
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standard error of the sample = square root(118 * 0.80 * (1-0.80)) = 4.3451
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since the sample size of 118 > 30, we can use the normal distribution approximation
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z-score = (90 - 94.4) / 4.3451 = -1.01
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Probability ( X < 90 ) = 0.1562
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if we choose to use the binomial probability formula and calculate the cumulative probability for X < or = 90, we get the following
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for n=118, successes=90, p=0.80
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Probability ( X < or = 90 ) = 0.1834
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the difference is due to the fact that the normal probability distribution is continuous and the binomial probability distribution is discrete
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