A Tire Company Finds The Lifespan For One Brand Of Its Tires Is Normally Distributed With A Mean Of 47,500

The approximate number of miles for a warranty is 41,748.57 miles.

What is Standard Deviation?

Standard deviation refers to the distribution’s extent of variability or dispersion. It is a measure of how much the data varies from the mean. It is represented by the Greek letter sigma (σ) and is used to calculate the data variability. It is the square root of the variance of a random variable that describes how widely the data points differ from the average value.

What should be the approximate number of miles for a warranty?

We have, Mean (μ) = 47,500 miles

Standard deviation (σ) = 3,000 miles

Manufacturer replacement threshold = 10% = 0.1

The number of miles for a warranty would have to be determined if the tire company wanted to replace no more than 10% of the tires.

Suppose x is the number of miles for which a warranty can be offered.

Using the standard normal distribution, we may compute the z-score as follows:

z = (x – μ) / σ

At the 10th percentile of the standard normal distribution, we’ll find the z-score. This z-score can be found using the standard normal distribution table or software.

At the 10th percentile, the z-score is -1.28 (from the table).

Now, substitute the given values.

z = (x – μ) / σ

-1.28 = (x – 47,500) / 3,000

Cross-multiplying and solving for x gives us:

x = -1.28 × 3,000 + 47,500x ⇒ 43,660 miles

Therefore, the tire company should offer a warranty for around 43,660 miles (approximated).

To know more about the “Standard deviation“: brainly.com/question/242980373

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