3 The Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire Tests reveal the mean mileage is 67900 with a standard deviation of 2050 miles and the distribution

To find the minimum guaranteed mileage, we need to find the value on the normal distribution that corresponds to the 4th percentile, or the point where only 4% of the tires will have to be replaced.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the 4th percentile is -1.75 (rounded to two decimal places).

We can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the minimum guaranteed mileage we want to find, μ is the mean mileage of 67,900, and σ is the standard deviation of 2,050.

Substituting the values, we get:

-1.75 = (x - 67,900) / 2,050

Multiplying both sides by 2,050, we get:

-3,577.5 = x - 67,900

Adding 67,900 to both sides, we get:

x = 64,322.5

Therefore, Layton should announce a minimum guaranteed mileage of 64,322.5 miles to ensure that no more than 4% of the tires will have to be replaced.