Answer:
The answer is "8.74 and 36.46 years"
Step-by-step explanation:
Mean (life-time)=22.6 years
standard deviation= 3.1 years
We must find out how many standard deviations are 95% of the data.
[tex]1 - \frac{1}{k^2} = 0.95\\\\1 - 0.95 = \frac{1}{k^2}\\\\\frac{1}{k^2} = 0.05\\\\\frac{1}{0.05} =k^2\\\\k^2 = 20\\\\ k = 4.47[/tex]
Calculating the lower limit and upper limit:
[tex]Lower\ limit = 22.6 - 4.47(3.1) = 22.6 - 13.86 = 8.74\\\\Upper\ limit = 22.6 + 4.47(3.1) = 22.6 + 13.86 = 36.46[/tex]
Limit is 8.74 years to 36.46 years
