Life expectancy

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

Correct answer:

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

Step-by-step explanation:

$$\begin{gathered} m=350\text{min} \\ \sigma =10\text{min} \\ {a}_1=m-1\cdot \sigma =350-1\cdot 10=340\text{min} \end{gathered}$$

$a_2=m+1\cdot \sigma =350+1\cdot 10=360\text{min}$

$b_1=m-3\cdot \sigma =350-3\cdot 10=320\text{min}$

$b_2=m+3\cdot \sigma =350+3\cdot 10=380\text{min}$

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