The amount of fill in a half-liter (500 ml) soft drink bottle is normally distri

Question

The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 7.0 ml. The mean is adjustable.

Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled?

Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled?

Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled?

Explanation / Answer

Let x is the required mean.
z = (x - 500)/7
P(z< 1.65) =0.95
P(z < (x - 500)/7) = 0.95 [Given]

(x - 500)/7 = 1.65
or, x = 1.65*7 + 500 = 511.55

Let x is the required mean.
z = (x - 500)/7
P(z< 2.32) =0.99
P(z < (x - 500)/7) = 0.99 [Given]

(x - 500)/7 = 2.32
or, x = 2.32*7 + 500 = 516.24

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