Question

The number of coughs during an 80-minute homework in a professor's statistics class has a Poisson distribution with a mean of 0.63 coughs per minute. What is the probability that at least one cough will occur in any given 5-minute time span? Give your answer to three decimal places. Hint: You will need to first find the mean number of coughs per five-minute span (λ) using the mean number of coughs per minute, μ.

Answer 1

Number of coughs during 80 minutes homework has Poisson distribution with

mean = 0.63 coughs per minute.

  =0.63

Let X be the number of coughs in 5 minutes period.

Then we need to find P (X>=1)

P (X>=1) = 1-P (X=0)

Here P (X=0)=(^X.e^-)÷X!

Here =mean number of coughs per 5 minutes = 0.63×5=3.15

P (X=0)=((3.15)^0. e^-3.15))÷0!

= 0.0429

P (X>=1)=1-0.0429=0.9571

Probability that atleast one cough will occur in 5 minutes period = 0.9571 answer.