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Alik [6]
3 years ago
12

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is no

rmally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce
Business
2 answers:
My name is Ann [436]3 years ago
7 0

Answer:

x = -1.6449*2050 + 47900 = 44,528

Explanation:

no more than 5 percent of the tires will have to be replaced...

then z = -1.6449

x = -1.6449*2050 + 47900 = 44,528

kogti [31]3 years ago
6 0

Answer:

The manufacturer should announce a guaranteed mileage of 44528 miles

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 47900, \sigma = 2050

What guaranteed mileage should the manufacturer announce

Only until the 5th percentile will have to be replaced, which is the value of X when Z has a pvalue of 0.05. So it is X when Z = -1.645.

Z = \frac{X - \mu}{\sigma}

-1.645 = \frac{X - 47900}{2050}

X - 47900 = -1.645*2050

X = 44528

The manufacturer should announce a guaranteed mileage of 44528 miles

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