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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

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

Beginner2021-11-29Added 11 answers

Step 1

Given data,

Rider can deliver 10 packages in 1 hour

$\lambda =10per\text{}hour$

For 30 mins$\lambda =\frac{10}{2}=5$

$P(X\le 4)=?$

Step 2

ByPoisson distribution

$P(X=x)=\frac{{e}^{-\lambda \times {\lambda}^{x}}}{x!}$

$P(X\le 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)$

$P(X=0)=\frac{{e}^{-5}\times {5}^{0}}{0!}=0.0067$

$P(X=1)=\frac{{e}^{-5}\times {5}^{1}}{1!}=0.0337$

$P(X=2)=\frac{{e}^{-5}\times {5}^{2}}{2!}=0.0842$

$P(X=3)=\frac{{e}^{-5}\times {5}^{3}}{3!}=0.1404$

$P(X=4)=\frac{{e}^{-5}\times {5}^{4}}{4!}=0.1755$

$P(X\le 4=0.4405)$

Option F is correct

Given data,

Rider can deliver 10 packages in 1 hour

For 30 mins

Step 2

ByPoisson distribution

Option F is correct