Beer bottles are filled so that they contain an average of 480 ml of beer in eac

Question

Beer bottles are filled so that they contain an average of 480 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml. Use Table 1.

What is the probability that a randomly selected bottle will have less than 474 ml of beer? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 474 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 12-pack of beer will have a mean amount less than 474 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Beer bottles are filled so that they contain an average of 480 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml. Use Table 1.

Explanation / Answer

Solution:- Given that  mean = 480 ml, Sd = 8 ml

a) P(X < 474) = P(z < (X - )/ )

= P(z < (474 - 480)/8)

= P(z < -0.75)

= 1P(Z < 0.75)

= 1 0.7734

= 0.2266

b.  P(x < 474) = P(z < (x - )/(/n)

=  P(z < (474 - 480)/(8/6))

=  P(z < -1.83)

= 1 P(Z < 1.83)

= 1 0.9664

= 0.0336

c. P(x < 474) = P(z < (x - )/(/n)

=  P(z < (474 - 480)/(8/12))

=   P(z < -2.60)

= 1 P(Z < 2.60)

= 1 0.9953

= 0.0047

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