# Life expectancy

The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last?
What is the range in minutes approximately 99.7% of batteries will last?

Correct result:

a1 =  340 min
a2 =  360 min
b1 =  320 min
b2 =  380 min

#### Solution:

$m=350 \ \text{min} \ \\ s=10 \ \text{min} \ \\ \ \\ a_{1}=m-1 \cdot \ s=350-1 \cdot \ 10=340 \ \text{min}$
$a_{2}=m+1 \cdot \ s=350+1 \cdot \ 10=360 \ \text{min}$
$b_{1}=m-3 \cdot \ s=350-3 \cdot \ 10=320 \ \text{min}$
$b_{2}=m+3 \cdot \ s=350+3 \cdot \ 10=380 \ \text{min}$

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