Question

The set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months. what is the life span of an appliance that has a z-score of –3?

Answer 1

Using the normal distribution, it is found that the life span of an appliance that has a z-score of –3 is of 24 months.

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.

In this problem, the parameters are given as follows:

$\mu = 48, \sigma = 8, Z = -3$.

Hence:

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

$-3 = \frac{X - 48}{8}$

X - 48 = -24

X = 24.

The life span of an appliance that has a z-score of –3 is of 24 months.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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