Question

27 A ferson with a cough is a persona non grata on airpianes, elevators, or at the theater. In theaters especilly, tbhe intaton level ries Cerlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 11 coughs per minute () Let- mumber of coughs in a given time interval, Explein why the Poisson distribution O Coughs would be agood choice for the probebility dstnibution of r are a rare occurrence. It is reasonable to assume the events are independent. are a rare occurrence. It is ressonable to assume the events are dependent O Coughs are a common occurrence. It is reasonable to assume the events are dependent. O Coughs are s common accurrence. is reasonable to assume the events are independent (b) Find the probability of four or fewer coughs (in α la auditanum) ม. 1-minute penod (use 4 mai places.) (e) Find the probability of at least four coughs Oin s large audnonium) in a 24-second period. (Use 4 decimal places)

Answer 1

b) For t = 1 munite r follows Poisson distribution with parameter $\lambda$ = 11*1 = 11

Here we want to find P( R <= 4)

Let's use excel:

P( R <= 4) = "=POISSON(4,11,1)" = 0.0151

c) For t = 24 second r follows Poisson distribution with parameter $\lambda$ = 11*(24/60) = 11*0.4 = 4.4

Here we want to find P( R >=  4) = 1 - P(R < 4) = 1 - P( R <= 3) .........( 1 )

Let's use excel:

P( R <= 3) = "=POISSON(3,4.4,1)" = 0.3594

Plug this value in equation ( 1 ), we get:

P( R >=  4) = 1 - 0.3594 = 0.6406