Mathematics, 02.07.2020 19:01 emory238
Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. Determine the probability that the child must wait between 6 and 9 minutes on the bus on a given morning.
Answers: 1
is the decay parameter.
.
![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](/tpl/images/0699/9878/a1573.png)
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