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? 3 months 24 months 45 months 72 months.

Answer 1

To solve the problem we must know about Z-Score.

What is Z-score?

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

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

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

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

Given to us

• Mean, μ = 48 months,
• standard deviation, σ = 8 months,
• Z-Score = -3

What is the life span of an appliance?

The life span of the appliance can be calculated using the Z-score formula,

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

Substitute the values,

$-3 = \dfrac{X- 48}{8}\\\\-3 \times 8 = X - 48\\\\-24+48=X\\\\X = 24\ months$

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

Learn more about Z-score:

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