Question

A soft drink company fills two-liter bottles on several
different lines of production equipment. The fill volume of its new
machine is normally distributed with a mean of 2.01 liters and a
variance of 0.04 liter^{2} .

a) Find the probability that a randomly selected two-liter bottle would contain between 1.98 and 2.06 liters.

b) The company want to define a minimum threshold of the fill volume so it can guarantee to their customers that 85% of their bottles are filled to the threshold above. Find the threshold.

Answer #1

a.

μ = 2.01, σ = 0.2

We need to compute Pr ( 1.98 ≤ X ≤ 2.06). The corresponding z-values needed to be computed are:

Therefore, we get:

the probability that a randomly selected two-liter bottle would contain between 1.98 and 2.06 liters is 0.1583

b.

The company wants to define a minimum threshold of the fill volume so it can guarantee to its customers that 85% of their bottles are filled to the threshold above the minimum threshold is 2.217287.

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