Question

Beer bottles are filled so that they contain an average of 475 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. What is the probability that a randomly selected bottle will have less than 469 ml of beer?

Answer 1

Answer:

22.66% probability that a randomly selected bottle will have less than 469 ml of beer

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 475, \sigma = 8$

What is the probability that a randomly selected bottle will have less than 469 ml of beer?

This is the pvalue of Z when X = 469. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{469 - 475}{8}$

$Z = -0.75$

$Z = -0.75$ has a pvalue of 0.2266.

22.66% probability that a randomly selected bottle will have less than 469 ml of beer