# Use Normal distribution Calculate probability

Feb 3rd, 2012
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The example problem goes: A landfill operation collects daily waste amounts, which are normally distributed with a mean of 26.4 tons and a standard deviation of 2.4 tons. for a randomly selected day... A) find the probability that the waste is less than 26.0 tons B) Find the probability that the amount is between 26.0 and 30.0 tons C) If the landfill is overburdened once the waste exceeds the top 5%of its capacity. Find the amount of waste which causes the landfill to be overburdened. D. For 40 randomly selected days, find the probability that the mean amount of waste is more than 25.8 tons.

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A landfill operation collects daily waste amounts, which are normally distributed with a mean of 26.4 tons and a standard deviation of 2.4 tons. for a randomly selected day...A) find the probability that the waste is less than 26.0 tonsB) Find the probability that the amount is between 26.0 and 30.0 tonsC) If the landfill is overburdened once the waste exceeds the top 5%of its capacity. Find the amount of waste which causes the landfill to be overburdened.D. For 40 randomly selected days, find the probability that the mean amount of waste is more than 25.8 tons.===========================In order to use standard normal distribution table to find the probability asked, we need to compute the z-score for the random variable X (with value x), by using the formula where ? is the mean and ? the standard deviation of X. Then x = ?+?Z, P (X?x) = P ( ?+?Z ?x)= P( ?Z?x-?)= P(Z? (x-?)/?

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