Question

QUESTION 13 Provide an appropriate response. Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12 39 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 1229 ounces of beer. 0.9938 0.5062 0.4938 0.0062

Answer 1

Let X be the amount of beer poured by filling machine.

Therefore,

X Nu = 12.39,0 = 0.04)

The probability that the bottle contains fewer than 12.29 ounces of beer is given by:

P(X < 12.29) = PX-M < 12.29 – 12.39 0,04

P(X < 12.29) = P(Z < -0.1 0.04

P(X < 12.29) = P(Z < -2.50)

### By using z table:

P(X < 12.29) = 0.0062