The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

A warranty of 6.185 years should be provided.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

The warranty should be the 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.55.

A warranty of 6.185 years should be provided.

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step-by-step explanation: