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exis [7]
2 years ago
9

The set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 mont

hs. what is the life span of an appliance that has a z-score of –3?
Mathematics
1 answer:
navik [9.2K]2 years ago
6 0

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.

<h3>Normal Probability Distribution</h3>

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 brainly.com/question/24663213

#SPJ4

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