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2021-11-28

On average, a J&T delivery rider can deliver 10 packages to their respective owners in one hour. Based on this data, what is the probability that the rider can deliver at most 4 packages in half an hour? Use Poisson distribution.
a. 0.9329
b. 0.7185
c. 0.2331
d. 0.6715
e. 0.2851
f. 0.4405
g. 0.5595
h. 0.6751

Edward Belanger

Step 1
Given data,
Rider can deliver 10 packages in 1 hour

For 30 mins $\lambda =\frac{10}{2}=5$
$P\left(X\le 4\right)=?$
Step 2
ByPoisson distribution
$P\left(X=x\right)=\frac{{e}^{-\lambda ×{\lambda }^{x}}}{x!}$
$P\left(X\le 4\right)=P\left(X=0\right)+P\left(X=1\right)+P\left(X=2\right)+P\left(X=3\right)+P\left(X=4\right)$
$P\left(X=0\right)=\frac{{e}^{-5}×{5}^{0}}{0!}=0.0067$
$P\left(X=1\right)=\frac{{e}^{-5}×{5}^{1}}{1!}=0.0337$
$P\left(X=2\right)=\frac{{e}^{-5}×{5}^{2}}{2!}=0.0842$
$P\left(X=3\right)=\frac{{e}^{-5}×{5}^{3}}{3!}=0.1404$
$P\left(X=4\right)=\frac{{e}^{-5}×{5}^{4}}{4!}=0.1755$
$P\left(X\le 4=0.4405\right)$
Option F is correct

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