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 3.5 ml. The mean is adjustable.

(a) Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)  

Mean             ml

(b) Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)  

Mean             ml

(c) Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)  

Mean             ml

Explanation / Answer

Solution:- s.d = 3.5ml

a.Let x is the required mean.
=> z = (x - 500)/3.5
P(z< 1.65) =0.95
P(z < (x - 500)/3.5) = 0.95

=> (x - 500)/3.5 = 1.65
or, x = 1.65*3.5 + 500 = 505.775 = 505.78(rounded)

b) => z = (x - 500)/3.5

P(z< 2.33) =0.99
P(z < (x - 500)/3.5) = 0.99

=> (x - 500)/3.5 = 2.33
or, x = 2.33*3.5 + 500 = 508.155 = 508.16(rounded)

c)

b) => z = (x - 500)/3.5

P(z< 3.09) =0.999
P(z < (x - 500)/3.5) = 0.999

=> (x - 500)/3.5 = 3.09
or, x = 3.09*3.5 + 500 = 510.815 = 510.82(rounded)

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