Question

company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16.7 years and a standard deviation of 2.4 years.
if the company wants to provide a warranty so that only 4.3% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty = years
enter your answer as a number accurate to 1 decimal place. answers obtained using exact z - scores or z - scores rounded to 3 decimal places are accepted.
question help: \\( \square \\) post to forum

Explanation:

Step1: Find the z - score

We want to find the z - score \(z\) such that \(P(X\lt x)=0.043\). Looking up the value \(0.043\) in the standard normal distribution table (or using a calculator with a normal - distribution function), the z - score is approximately \(z=-1.72\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 16.7\) (mean), \(\sigma = 2.4\) (standard deviation), and \(z=-1.72\).
We can solve for \(x\):

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Answer:

\(12.6\)