4 years ago

X

Mathematics

1 answer:

Sergeu [11.5K]4 years ago

3 0

Answer:

0.33

Step-by-step explanation:

I just took the quiz

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3 years ago

Molecules of a toxic chemical eventually decompose into inert substances. Suppose the decomposition time is exponentially distri

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b) 27.73 years

c) 238.44 years

d) 3,870.53 years

Step-by-step explanation:

Let X be the random variable that measures the decomposition time.

$\bf \lambda =6$

In this case, since the decomposition time is exponentially distributed with a mean of 1/6, we have

$\bf P(X\leq t)=1-e^{-t/6}\Rightarrow P(X>t)=1-(1-e^{-t/6})=e^{-t/6}$

and we must find a t such that P(x>t)=0.5.

$\bf P(X>t)=0.5\Rightarrow e^{-t/6}=0.5\Rightarrow -t/6=ln(0.5)\Rightarrow t=-6ln(0.5)=4.16\;years$

$\bf \lambda =40$

$\bf P(X>t)=0.5\Rightarrow e^{-t/40}=0.5\Rightarrow -t/40=ln(0.5)\Rightarrow t=-40ln(0.5)=27.73\;years$

$\bf \lambda =344$

$\bf P(X>t)=0.5\Rightarrow e^{-t/344}=0.5\Rightarrow -t/344=ln(0.5)\Rightarrow t=-344ln(0.5)=238.44\;years$

$\bf \lambda =5584$

$\bf P(X>t)=0.5\Rightarrow e^{-t/5584}=0.5\Rightarrow -t/5584=ln(0.5)\Rightarrow t=-5584ln(0.5)=3870.53\;years$

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Question 6

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Step-by-step explanation:

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