Question

The density function of the continuous random variable $X$, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is egin{equation} f(x) = egin{cases} frac{x}{9}, & 0 < x < 3, \ 5 - x, & 4 le x < 5, \ 0, & ext{elsewhere}. end{cases} end{equation} For both parts (a) and (b) below, express your final answers in hours. (a) Find the average number of hours per year that families run their vacuum cleaners. (b) Find the standard deviation of the number of hours per year that families run their vacuum cleaners.

          The density function of the continuous random variable $X$, the total number of hours, in
units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is
egin{equation*}
f(x) = egin{cases}
frac{x}{9}, & 0 < x < 3, \
5 - x, & 4 le x < 5, \
0, & 	ext{elsewhere}.
end{cases}
end{equation*}
For both parts (a) and (b) below, express your final answers in hours.
(a) Find the average number of hours per year that families run their vacuum cleaners.
(b) Find the standard deviation of the number of hours per year that families run their
vacuum cleaners.

$The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is eginequation* f(x) = egincases fracx9, 0 < x < 3, 5 - x, 4 le x < 5, 0, extelsewhere. endcases endequation* For both parts (a) and (b) below, express your final answers in hours. (a) Find the average number of hours per year that families run their vacuum cleaners. (b) Find the standard deviation of the number of hours per year that families run their vacuum cleaners.$

Added by Linda F.

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