Question

Beer bottles are filled so that they contain an average of 385 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 9 ml. Use Table 1.

a.	What is the probability that a randomly selected bottle will have less than 380 ml of beer?(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

b.	What is the probability that a randomly selected 7-pack of beer will have a mean amount less than 380 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

c.	What is the probability that a randomly selected 24-pack of beer will have a mean amount less than 380 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 385

standard deviation = = 9

a.

P(x < 380) = P[(x - ) / < (380 - 385) / 9]

= P(z < -0.56)

= 0.2877

Probability = 0.2877

b.

n = 7

= 385

= / n = 9 / 7 = 3.4017

P( < 380) = P(( - ) / < (380 - 385) / 3.4017)

= P(z < -1.47)

= 0.0708

Probability = 0.0708

c.

n = 24

= 385

= / n = 9 / 24 = 1.8371

P( < 380) = P(( - ) / < (380 - 385) / 1.8371)

= P(z < -2.72)

= 0.0033

Probability = 0.0033