Question

Laundry detergent boxes are filled according to an approximately Normal distribution with mean 34.15 ounces and standard deviation 0.1 ounces. What is the probability a randomly selected box has less than the 34 ounces of advertised weight?

Answer 1

Using the normal distribution, it is found that there is a 0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 34.15, \sigma = 0.1$.

The probability a randomly selected box has less than the 34 ounces of advertised weight is the p-value of Z when X = 34, hence:

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

$Z = \frac{34 - 34.15}{0.1}$

Z = -1.5

Z = -1.5 has a p-value of 0.0668.

0.0668 = 6.68% probability a randomly selected box has less than the 34 ounces of advertised weight.

More can be learned about the normal distribution at brainly.com/question/24537145

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