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 6.0 ml. The mean is adjustable.

(a) Where should the mean be set to ensure a 90 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 95 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 99.0 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)

Mean ml

Explanation / Answer

Formula: Z = (X - mean)/SD

a) P(X > x) = 0.9
P(X < x) = 0.1

P(Z < (x - 500)/6) = 0.1
(x - 500)/6 = -1.28
x = 492.32

b) P(X > x) = 0.95

P(X < x) = 0.05

P(Z < (x - 500)/6) = 0.05
(x - 500)/6 = -1.64
x = 490.16

c)

P(X > x) = 0.99

P(X < x) = 0.01

P(Z < (x - 500)/6) = 0.01
(x - 500)/6 = -2.33
x = 486.02

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