XB 70 Tire Mileage Guarantee

B

Find the z-value for an area under the curve of 1.0 - 0.55 = 0.45. For an area of 0.45, z = -1.645. Using z = (x-u)/sigma. -1.645 = x - 47900/2050. x = 44528.

To determine the guaranteed mileage that the manufacturer should announce, we need to find the mileage value at which no more than 5 percent of the tires will have to be replaced. This involves finding the cutoff point of the distribution that corresponds to the 95th percentile.

Given that the mean mileage is 47,900 and the standard deviation is 2,050, we can use the concept of z-scores and the standard normal distribution to find the cutoff point.

The z-score is a measure of how many standard deviations a particular value is away from the mean. We can calculate the z-score using the formula:

z = (x - μ) / σ

Where:

• z is the z-score
• x is the value we want to find the cutoff for (guaranteed mileage)
• μ is the mean mileage (47,900)
• σ is the standard deviation (2,050)

To find the cutoff point corresponding to the 95th percentile, we need to find the z-score for which the cumulative area under the standard normal distribution is 0.95. In other words, we want to find the z-score that leaves 5 percent of the distribution in the tail.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to a cumulative area of 0.95 is approximately 1.645.

Now, we can rearrange the z-score formula to solve for x (guaranteed mileage):

x = z * σ + μ

Plugging in the values:

x = 1.645 * 2,050 + 47,900

x ≈ 3,373.25 + 47,900

x ≈ 51,273.25

Since the mileage value must be an integer, the manufacturer should round down the guaranteed mileage to the nearest whole number.

The correct answer would be C. 49,621.

None of the provided answer choices exactly match the calculated guaranteed mileage.