Question

The life (in months) of a certain electronic computer part has a probability density function defined by $f(t) = \frac{1}{4}e^{-\frac{t}{4}}$ for t in $[0, \infty)$. Find the probability that a randomly selected component will last the following lengths of time. Complete parts (a) through (d). a. At most 16 months The probability that the component will last at most 16 months is (Round to four decimal places as needed.) b. Between 12 and 16 months The probability that the component will last between 12 and 16 months is . (Round to four decimal places as needed.) c. Find the cumulative distribution function for this random variable. F(t) = (Type an expression using t as the variable.) What is the domain of the cumulative distribution function? The domain is . (Type your answer in interval notation.) d. Use the answer to part (c) to find the probability that a randomly selected component will last at most 8 months. The probability that the component will last at most 8 months is . (Round to four decimal places as needed.)

          The life (in months) of a certain electronic computer part has a probability density function defined by
$f(t) = \frac{1}{4}e^{-\frac{t}{4}}$ for t in $[0, \infty)$.
Find the probability that a randomly selected component will last the following lengths of time. Complete parts (a) through (d).
a. At most 16 months
The probability that the component will last at most 16 months is 
(Round to four decimal places as needed.)
b. Between 12 and 16 months
The probability that the component will last between 12 and 16 months is .
(Round to four decimal places as needed.)
c. Find the cumulative distribution function for this random variable.
F(t) = 
(Type an expression using t as the variable.)
What is the domain of the cumulative distribution function?
The domain is .
(Type your answer in interval notation.)
d. Use the answer to part (c) to find the probability that a randomly selected component will last at most 8 months.
The probability that the component will last at most 8 months is .
(Round to four decimal places as needed.)

The life (in months) of a certain electronic computer part has a probability density function defined by
f(t) = (1)/(4)e^-(t)/(4) for t in [0, ∞).
Find the probability that a randomly selected component will last the following lengths of time. Complete parts (a) through (d).
a. At most 16 months
The probability that the component will last at most 16 months is
(Round to four decimal places as needed.)
b. Between 12 and 16 months
The probability that the component will last between 12 and 16 months is .
(Round to four decimal places as needed.)
c. Find the cumulative distribution function for this random variable.
F(t) =
(Type an expression using t as the variable.)
What is the domain of the cumulative distribution function?
The domain is .
(Type your answer in interval notation.)
d. Use the answer to part (c) to find the probability that a randomly selected component will last at most 8 months.
The probability that the component will last at most 8 months is .
(Round to four decimal places as needed.)

Added by Jeffery D.

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