In a certain chemical process three bottles of a standard fluid are emptied into

Question

In a certain chemical process three bottles of a standard fluid are emptied into a larger container. A study of the individual bottles shows that the mean value of the contents is 15 ounces and value and the standard deviation is 0.08 ounces. If three bottles form a random sample, (a) Find the expected value and the standard deviation of the volume of liquid emptied into the larger container. (b) If the content of the individual bottles is normally distributed, what is the probability that the volume of liquid emptied into the larger container will be in excess of 45.2 ounces?

Explanation / Answer

Mean is 15 and standard deviation is 0.08 and n=3

a) Expected value is given by mean which is 15

Standard deviation is given by 0.08/sqrt(3)= 0.0462

b) P(x>45.2)= P(z>(45.2-45)/0.0462)=P(z>4.33) which is 1

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