The working lifetime, in years, of a particular model of bread maker is normally distributed with mean 10 and variance 4. Calculate the 12th percentile of the working lifetime, in years.

The 12th percentile of the working lifetime is 7.65 years.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation(which is the square root of the variance) , 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:

12th percentile:

X when Z has a pvalue of 0.12. So X when Z = -1.175.

The 12th percentile of the working lifetime is 7.65 years.

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