The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months Assume the lives of dishwashers are normally distributed.
a) What are the minimum and maximum life expectancy of the middle 95% of the dishwashers' lives (give answer in months)

Question

The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months Assume the lives of dishwashers are normally distributed. 
a) What are the minimum and maximum life expectancy of the middle 95% of the dishwashers' lives (give answer in months)

holsteremission · Answer

If you're familiar with the empirical rule for normal distributions, you may know that $95\%$ of a normal distribution falls within two standard deviations of the mean. So if the mean is $\mu$ and the standard deviation is $\sigma$, then $95\%$ of the distributions falls in the interval $(\mu-2\sigma,\mu+2\sigma)$. The rule I'm referring to is this one: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule