Random variables- Poisson distribution

[ag78]

The number of orders for a certain item received daily at a warehouse is a random
variable with a Poisson distribution of parameter 4.
a) What is the probability that, in one day, you will receive more than 3 and
less than 8 orders?
b) In one day, what is the most likely number of orders?
c) How many items must be in the warehouse daily, so that it is possible to
satisfy all orders in at least 80% of the cases?
d) What is the probability of over the course of a week (5 working days):
i) the number of orders exceed 20?a
ii) Is there at least 1 day when the number of orders is 4?

 

[tkhunny]

Please show YOUR work. Here are some hints.

The number of orders for a certain item received daily at a warehouse is a random
variable with a Poisson distribution of parameter 4.

a) What is the probability that, in one day, you will receive more than 3 and less than 8 orders?

Calculate p(4)+p(5)+p(6)+p(7)

b) In one day, what is the most likely number of orders?

This is given in the problem statement.

c) How many items must be in the warehouse daily, so that it is possible to satisfy all orders in at least 80% of the cases?

Calculate p(0)+p(1)+p(2),+p(3) + ... + p(n) > 0.80 and report the number "n".

d) What is the probability of over the course of a week (5 working days):
i) the number of orders exceed 20?

The Poisson Distribution is perfectly scalable. [math]5\cdot\lambda_{day} = \lambda_{WorkWeek}[/math]

ii) Is there at least 1 day when the number of orders is 4?

Strange question. It is a probability, not an assurance.