Life tests performed on a sample of 100 batteries indicated: (1) an average life of 75 months, (2) a standard deviation of 5 months, and (3) a bell shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use? The answer is 2.5% just wondering how to get there?
2026-04-02 10:44:32.1775126672
Intro to Stats Question
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With a 'normal' (bell-shaped) distribution, about 95% of all batteries' lifespan lie within two standard deviations of the mean. In other words, about 95% have a life span between $75-2*5=65$ and $75+2*5=85$ months. And that means that about 5% have a lifespan that lies outside that interval, with about half of that (i.e 2.5%) below 65 months and the other half (i.e 2.5%) over 85 months. These are all rough approximations though.