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 4.5 ml. The mean is adjustable.

(Round to 2 decimal places)

(a)    

Where should the mean be set to ensure a 90 percent probability that a half-liter bottle will not be underfilled? ml

(b)  

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

(c)  

Where should the mean be set to ensure a 99.0 percent probability that a half-liter bottle will not be underfilled? ml

Explanation / Answer

a)

Note that

u = x - z*sigma

For a 1-0.90 = 0.10 left tailed area, the z score corresponding to it is

z = -1.281551566

Thus,

u = x - z*sigma = 500 - (-1.281551566)*4.5

u = 505.766982 [ANSWER]

***********************

b)

Note that

u = x - z*sigma

For a 1-0.95 = 0.05 left tailed area, the z score corresponding to it is

z = -1.644853627

Thus,

u = x - z*sigma = 500 - (-1.644853627)*4.5

u = 507.4018413 [ANSWER]

*************************

c)

Note that

u = x - z*sigma

For a 1-0.99 = 0.01 left tailed area, the z score corresponding to it is

z = -2.326347874

Thus,

u = x - z*sigma = 500 - (-2.326347874)*4.5

u = 510.4685654 [ANSWER]

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