Question

If the dealer wants to give warranty to 32% of customer. Mean

tire 32000, std =2500 what's the mileage should he give?

Answer 1

To determine the mileage the dealer should offer to provide a warranty to 32% of customers, you can use the standard normal distribution (z-score).

Given that the mean (μ) mileage is 32,000 and the standard deviation (σ) is 2,500, you want to find the mileage (x) such that the cumulative probability up to x corresponds to 32%.

1. Find the z-score using the formula: \[ z = \frac{{x - \mu}}{{\sigma}} \]

2. Look up the z-score in a standard normal distribution table to find the corresponding cumulative probability.

For a cumulative probability of 32%, you are looking for the z-score that corresponds to 0.32.

Once you find the z-score, use it to find the corresponding mileage (x):

\[ x = z \times \sigma + \mu \]

This will give you the mileage the dealer should offer to provide a warranty to 32% of customers.

Answer 2

To determine the mileage that the dealer should give for warranty to 32% of customers, we can use the standard normal distribution and z-scores. By finding the z-score that corresponds to a cumulative probability of 0.32, we can calculate the mileage value. In this case, the mileage should be approximately 46459 miles.

Step-by-step explanation:

To determine the mileage that the dealer should give for warranty, we first need to find the z-score corresponding to the desired percentage of customers.

Using the formula:
z = (x - mean) / std

where x is the desired mileage, mean is the average mileage of the tires, and std is the standard deviation of the tires.

Let's substitute the given values:
z = (x - 46500) / 9800

Since we want to find the mileage that corresponds to 32% of customers, we need to find the z-score that corresponds to a cumulative probability of 0.32.

Referring to the standard normal distribution table, we find that the z-score is approximately -0.47.

Substituting this value back into the z-score formula, we can solve for x:

-0.47 = (x - 46500) / 9800

Solving for x, we get:

x = -0.47 * 9800 + 46500

x ≈ 46459 miles