Empirical Rule

Use the Empirical Rule to find the following probabilities. It is suggested that you draw a normal curve, label the $x-$values for $1,2,$ and $3$ standard deviations from the mean, and write in the probabilities between each standard deviation before attempting to answer the questions.

The average life$-$span of a True Test auto battery is $39$ months with a standard deviation of $3$ months.

Assume a normal distribution.

We can expect $95\%$ of the batteries to last

$\backslash$table$[[$between$,$and,months.$],[2.$ We can expect,$\%$ of the batteries to$,]]$

last less than $30$ months.

$3.$ We can expect $\%$ of the batteries to last longer than $42$ months.

$4.$ We can expect $\%$ of the batteries to last between $30$ and $39$ months.

$5.$ We can expect $\%$ of the batteries to last between $42$ and $48$ months.