Question

Beer bottles are filled so that they contain an average of 455 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 6 ml. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected bottle will have less than 452 ml of beer? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 452 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What is the probability that a randomly selected 12-pack of beer will have a mean amount less than 452 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 455

standard deviation = = 6

a.

P(x < 452) = P[(x - ) / < (452 - 455) / 6]

= P(z < -0.5)

= 0.3085

Probability = 0.3085

b.

= / n = 6 / 6 = 2.4495

P( < 455) = P(( - ) / < (452 - 455) / 2.4495)

= P(z < -1.22)

= 0.1112

Probability = 0.1112

c.

= / n = 6 / 12 = 1.7321

P( < 452) = P(( - ) / < (452 - 455) / 1.7321)

= P(z < -1.73)

= 0.0418

Probability = 0.0418