Question

Beer bottles are filled so that they contain an average of 335 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. What is the probability that a randomly selected bottle will have less than 332 ml of beer?

Answer 1

To find the probability that a randomly selected bottle will have less than 332 ml of beer, use the z-score formula and the standard normal distribution table.

Step-by-step explanation:

To find the probability that a randomly selected bottle will have less than 332 ml of beer, we need to calculate the z-score and then find the corresponding area under the normal distribution curve.

The z-score formula is given by: z = (x - μ) / σ

Where x is the value we are interested in (332 ml), μ is the mean (335 ml), and σ is the standard deviation (7 ml).

Substituting the values into the formula, we get: z = (332 - 335) / 7 = -0.429

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = -0.429 is approximately 0.3336.

Therefore, the probability that a randomly selected bottle will have less than 332 ml of beer is approximately 0.3336 or 33.36%.