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?

Result

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

Solution:

m=350 min s=10 min  a1=m1 s=3501 10=340 minm=350 \ \text{min} \ \\ s=10 \ \text{min} \ \\ \ \\ a_{1}=m-1 \cdot \ s=350-1 \cdot \ 10=340 \ \text{min}
a2=m+1 s=350+1 10=360 mina_{2}=m+1 \cdot \ s=350+1 \cdot \ 10=360 \ \text{min}
b1=m3 s=3503 10=320 minb_{1}=m-3 \cdot \ s=350-3 \cdot \ 10=320 \ \text{min}
b2=m+3 s=350+3 10=380 minb_{2}=m+3 \cdot \ s=350+3 \cdot \ 10=380 \ \text{min}



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