Poisson

IAL S2 Poisson Distribution

Discrete Probability Distribution
"How many events occur within some period of time, given an average rate λ (“lambda”) of occurence."

Multiple Choice

The Binomial distribution can be defined as:

"The number of “successes” out of n independent trials, each with a probability p of success"

• True

• False

Multiple Choice

In a random sample of 100 people, the probability of studying Maths is 0.3. What is the probability of 18 people studying Maths?

• Binomial

• Poisson

• Neither

Multiple Choice

An instagram account receives 5 likes every 10 minutes. What is the probability of receiving 20 likes in an hour?

• Binomial

• Poisson

• Neither

Multiple Choice

A volcano erupts every 1000 years, and we’re interested in the probability of at least one eruption next year.

• Binomial

• Poisson

• Neither

Page 20 in your Formula Booklet! :)

Fill in the Blank

$$X\sim Po\left(1.2\right)$$   

What is P(X=3)? (3sf)

Fill in the Blank

Given that an Instagram account receives 25 likes an hour on average, determine the probability it receives 20 likes in the next hour.

Fill in the Blank

$$Y\sim Po\left(0.35\right)$$  
$$P\left(1\le Y<3\right)$$  

Fill in the Blank

On average 8 cars come down a country road an hour. What’s the probability that: Less than 5 cars pass in the next hour? 

Open Ended

A website receives hits at a rate of 300 per hour.

State two reasons why a Poisson Distribution model can be used.

Multiple Select

Select which Binomial Distributions can be approximated with Poisson

• $$X\sim B\left(100,\ 0.1\right)$$  

• $$X\sim B\left(50,\ 0.5\right)$$  

• $$X\sim B\left(40,\ 0.02\right)$$  

• $$X\sim B\left(300,\ 0.2\right)$$  

Multiple Choice

Poisson Formula: P(X=x)

Multiple Choice

X is Poisson Distribution. Mean & Variance formula

Multiple Choice

Poisson is a __________ probability distribution

• random

• discrete

• continuous