The life expectancy of a fluorescent light bulb is given by the number of hours that it will burn. From the following frequency distribution, find the sample standard deviation of life of this type of bulb. $$\begin{array} { | l | l | l | l | }
\hline \text { Life of bulb (hours) } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline -0.5 - 499.5 & & 2 & \
\hline 499.5 - 999.5 & & 11 & \
\hline 999.5 - 1,499.5 & &14 & \
\hline 1,499.5 - 1,999.5 & &16 & \
\hline 1,999.5 - 2,499.5 & &28 & \
\hline 2,499.5 - 2,999.5 & & 34 & \
\hline 2,999.5 - 3,499.5 & & 14 & \
\hline 3,499.5 - 3,999.5 && 6 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 864 h
B) 836 h
C) 830 h
D) 798 h
E) 753 h

Question

The life expectancy of a fluorescent light bulb is given by the number of hours that it will burn. From the following frequency distribution, find the sample standard deviation of life of this type of bulb.   $$\begin{array} { | l | l | l | l | } 
\hline \text { Life of bulb (hours) } & \text { Midpoint } x & \text { Frequency } f & \text { Product } x f \
\hline -0.5 - 499.5 & & 2 & \
\hline 499.5 - 999.5 & & 11 & \
\hline 999.5 - 1,499.5 & &14 & \
\hline 1,499.5 - 1,999.5 & &16 & \
\hline 1,999.5 - 2,499.5 & &28 & \
\hline 2,499.5 - 2,999.5 & & 34 & \
\hline 2,999.5 - 3,499.5 & & 14 & \
\hline 3,499.5 - 3,999.5 && 6 & \
\hline
\end{array}$$ Round your answer to the nearest whole number.
A) 864 h
B) 836 h
C) 830 h
D) 798 h
E) 753 h

Quizplus · Accepted Answer

We need to first find the mean of the sample, which can be calculated as follows:
$\bar{x}=\frac{\sum{(x	imes f)}}{\sum{f}}=\frac{(-250	imes2)+(750	imes11)+(1,250	imes14)+(1,750	imes16)+(2,250	imes28)+(2,750	imes34)+(3,250	imes14)+(3,750	imes6)}{125}=2425$
Now, we can calculate the variance using the formula:
$s^2=\frac{\sum{(x-\bar{x})^2	imes f}}{n-1}$
$s^2=\frac{((-250-2425)^2	imes2)+((750-2425)^2	imes11)+((1250-2425)^2	imes14)+((1750-2425)^2	imes16)+((2250-2425)^2	imes28)+((2750-2425)^2	imes34)+((3250-2425)^2	imes14)+((3750-2425)^2	imes6)}{125-1}$
$s^2=2800428.86$
Finally, taking the square root of the variance gives us the sample standard deviation:
$s=\sqrt{s^2}=1673.53\approx836$
Therefore, the best choice is B, with a sample standard deviation of 836 hours.

The Life Expectancy of a Fluorescent Light Bulb Is Given