Central Limit Theorem problem. When a certain chemical product is prepared the a

Question

Central Limit Theorem problem. When a certain chemical product is prepared the amount of a certain impurity is a random variable with a mean of 4 grams and a standard deviation of 2 grams. If 100 independent batches of the chemical are produced what is the (approximate) probability of the average amount of the impurity in the 100-batch sample being more that 4.5 grams? Central Limit Theorem problem. When a certain chemical product is prepared the amount of a certain impurity is a random variable with a mean of 4 grams and a standard deviation of 2 grams. If 100 independent batches of the chemical are produced what is the (approximate) probability of the average amount of the impurity in the 100-batch sample being more that 4.5 grams?

Explanation / Answer

population mean,u = 4

population standard deviation,,s = 2

sample size,n = 100

x = 4.5

z = (x-u) / (s/sqrt(n))

z = 2.50

P(X>4.5) = P(Z>2.50)

= 1 - P(Z<2.50)

= 1 - 0.9938

= 0.0062

Please rate my answer, good luck...

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