Mathematics, 12.02.2020 03:57 aliami0306oyaj0n
Suppose that, after measuring the duration of many telephone calls, a telephone company found their data was well-approximated by the density function p(x) = 0.1 e^-0.1x, where x is the duration of a call, in minutes. What percentage of calls last between 2 and 3 minutes? Percent = percent What percentage of calls last 2 minutes or less? Percent = percent What percentage of calls last 4 minutes or more? Percent = percent What is the cumulative distribution function, P(t)? P(t) =
Answers: 3
![=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%](/tpl/images/0508/0554/42bb3.png)
![=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%](/tpl/images/0508/0554/701cb.png)
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Suppose that, after measuring the duration of many telephone calls, a telephone company found their...
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