Chapter 9.2, Problem 34E

a)

To determine

To calculate: The probability that truck can be unloaded in less than 1 hour when the length of time needed to unload trucks at a depot is exponentially distributed with $\lambda =\frac{3}{4}$ by using the exponential probability density function given as,

$f\left(t\right)=\frac{1}{\lambda }{e}^{-t/\lambda }\text{, }\left[0,\infty \right)$

b)

To determine

To calculate: The probability that truck can be unloaded in more than 1 hour but less than 2 hour when the length of time needed to unload trucks at a depot is exponentially distributed with $\lambda =\frac{3}{4}$ by using the exponential probability density function given as,

$f\left(t\right)=\frac{1}{\lambda }{e}^{-t/\lambda }\text{, }\left[0,\infty \right)$

c)

To determine

To calculate: The probability that truck can be unloaded in at most 3 hours when the length of time needed to unload trucks at a depot is exponentially distributed with $\lambda =\frac{3}{4}$ by using the exponential probability density function given as,

$f\left(t\right)=\frac{1}{\lambda }{e}^{-t/\lambda }\text{, }\left[0,\infty \right)$