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Hi! I've been stuck on this question for a while. I know that I have to do some sort of 1-1/k^2 for empirical rule, correct? I can't figure out how to calculate any of this and what it means of within the standard deviation. I would greatly appreciate any help on this - thank you very much!

The mean life of a brand of auto batteries is 44 months with a standard deviation of 3 months. Assume that the lives of all auto bateries of this brand have a bell-shaped distribution.

1. using empirical rule, find the percentage of auto batteries of this brand that have a life of
a. 41 to 47 months
b. 35 to 53 months

2. using empirical rule, find the interval that contains the mean life of the batteries by 95% of the batteries.

3. One customer says that he used the battery for 52 months. Find the z-score for the 52 month.

I donft know about the 1-1/k^2 empirical rule. However, you can answer all of the questions by using Z scores.

Z = (X - ƒÊ)/SD

where X = raw score, ƒÊ = mean and SD = standard deviation.

Figure the Z scores for each of the raw scores and look up the percentages cut off in the normal distribution. This can be found in a table in the back of your statistics textbook.

I hope this helps. Thanks for asking.

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