# 02_16 - h What is the probability that there will be...

This preview shows pages 1–3. Sign up to view the full content.

STAT 400 Examples for 02/16/2011 Spring 2011 Poisson Distribution : X = the number of occurrences of a particular event in an interval of time or space. P( X = x ) = ! λ λ x x e - , x = 0, 1, 2, 3, … . E( X ) = λ , Var( X ) = λ . Table III ( pp. 580 – 582 ) gives P( X x ) EXCEL: = POISSON( x , λ , 0 ) gives P( X = x ) = POISSON( x , λ , 1 ) gives P( X x ) 1. Traffic accidents at a particular intersection follow Poisson distribution with an average rate of 1.4 per week. a) What is the probability that the next week is accident-free? b) What is the probability that there will be exactly 3 accidents next week? c) What is the probability that there will be at most 2 accidents next week?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
d) What is the probability that there will be at least 2 accidents during the next two weeks? e) What is the probability that there will be exactly 5 accidents during the next four weeks? f) What is the probability that there will be 2 accidents tomorrow? g) What is the probability that the next accident will not occur for three days?
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: h) What is the probability that there will be exactly two accident-free weeks during the next four weeks? When n is large ( n ≥ 20 ) and p is small ( p ≤ 0.05 ) and n ⋅ p ≤ 5, Binomial probabilities can be approximated by Poisson probabilities. For this, set λ = n ⋅ p . 2. Suppose the defective rate at a particular factory is 1%. Suppose 50 parts were selected from the daily output of parts. Let X denote the number of defective parts in the sample. a) Find the probability that the sample contains exactly 2 defective parts. b) Use Poisson approximation to find the probability that the sample contains exactly 2 defective parts. c) Find the probability that the sample contains at most 1 defective part. d) Use Poisson approximation to find the probability that the sample contains at most 1defective part....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

02_16 - h What is the probability that there will be...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online