Get the answer to "On average, a J&T delivery rider can deliver..."

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Answered question

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

Answer & Explanation

Edward Belanger

Beginner2021-11-29Added 11 answers

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

λ = 10 p e r h o u r

For 30 mins

λ = \frac{10}{2} = 5

P (X \leq 4) = ?

Step 2
ByPoisson distribution

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

P (X \leq 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 \leq 4 = 0.4405)

Option F is correct

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