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 and standard deviation
, the zscore of a measure X is given by:
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:
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.
The manufacturer should announce a guaranteed mileage of 44528 miles