Question

Cans of soft drink are filled by a machine that does not always give exactly the same fill every time. Suppose that the contents of 375 ml cans of one particular brand actually come from a Normal distribution with a mean of 379.2 ml and a standard deviation of 3.5 ml. If you choose a can at random and measure its contents, what is the probability that its contents are 375 ml or more?

Hint: You need to standardise this problem and convert it to a problem involving Z (which is a Normal variabe with a mean of 0 and a standard deviation of 1). Look at the examples in the Study Guide.

		0.3477
		0.6523
		0.8849
		0.1151
		0.9362

Answer 1

Consider that X represents the content in a soft drink can. The formula and calculation of the probability is as shown below: p(X 2375)-- 375-379.2 3.5 =p(Z>-1.2) =1-p(Z<-1.2) The calculation ofp (Z <-1.2) in Excel is as shown below: fNORMSDIST(-1.2) 0.1151 (Note: This probability can be also found by using standard normal table.) Therefore, p(X2 375) 1-p Z<-1.2) =1-0.1151 -0.8849 Hence the probability that a randomly chosen can will have 375 ml or more contents is 0.8849