Question

A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of tune, an average of 28 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives m a particular one second period. Round your answer to four decimals. Find the probability that at least two particles arrive in a particular 2 second period. Round your answer to four decimals. The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 19 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes? Give your answer accurate to two decimal places.

Answer 1

Answer:

Part I

p(x=1)=0.0000

p(x=2)=0.0000

Part II

p(x)=0.11

Step-by-step explanation:

For Poisson distribution:

$p(X=x)=e^-m\frac{m^x}{x!}$

Where m=mean, x=number of events

Given x=1, and mean,m=28

$p(X=1)=\frac{e^{-28} *28^1}{1!}\\p(X=1)=0.0000$

For x=2 and mean,m=28

$p(X=2)=\frac{e^{-28} *28^2}{2!}\\p(X=2)=0.0000$

For Uniform Distribution

Time interval 10 and 19 minutes is 9

Time interval between 15 and 16 minutes is 1

Therefore:-

$p(x)=\frac{1}{9}\\p(x)=0.1111\\p(x)=0.11 \ (2d.p)$