Drums labeled 30 L are filled with a solution from a large vat. The amount of so

Question

Drums labeled 30 L are filled with a solution from a large vat. The amount of solution put into each drum is ran- dom, with true mean 30.01 L and standard deviation 0.1 L.

(a) What is the probability that the total amount of so- lution contained in 50 drums is more than 1500 L?

(b) If the total amount of solution in the vat is 2401 L, what is the probability that 80 drums can be filled without running out?

(c) How much solution should the vat contain so that the probability is 0.90 that 80 drums can be filled without running out?

(d) Find the 10th percentile for the total amount of so- lution for 80 drums.

Explanation / Answer

A) by applying the Central Limit Theorem:

n = 50

S = "Total amount of solution in 50 drums"

The total amount of solution in n will have a mean of n x mean = 50 x 30.01, and a variance = 50 x 0.01 = 0.5 Using this values I'm able to calculate P(S > 1500) by approximating to a Standard Normal Distribution and checking on the cumulative table, obtaining a result of 0.758.

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