Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$. Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$.
A) 864665
B) $.950213$
C) 049787
D) .716531

Question

Quizplus · Accepted Answer

For an exponential distribution, the mean ($\mu$) and standard deviation ($\sigma$) are both equal to $\theta$. Therefore, $\mu = \sigma = 1.5$. The interval $\mu \pm 2\sigma$ translates to $1.5 \pm 3$, or $-1.5$ to $4.5$, but since negative values are not possible for an exponential distribution, we only consider the upper limit of $4.5$. The probability that $x$ will assume a value within $\mu \pm 2\sigma$ for any normal or approximately normal distribution (and by extension, using the empirical rule for exponential distributions in a broad sense) is approximately 95%. Hence, the closest answer is $.950213$.

Suppose That the Random Variable xxx Has an Exponential Distribution With θ=1.5\theta = 1.5θ=1.5

Suppose That the Random Variable $x$ Has an Exponential Distribution With $\theta = 1.5$