Question

(This is a long one, any answer is much appreciated!)

Scenario 6

The mean number of business failures in a month is 10. Assume failure rates are the same for any month and are independent of one another. Use Excel to find the following probabilities. (Round probabilities to four decimals).

1) What is the probability of 4 failures in a month?

2) What is the probability of 10 failures in a month?

3) What is the probability of 12 failures in a month?

4) What is the probability of less than 8 failures in a month?

5) What is the probability of 16 failures in two months?

Answer 1

1)

this is Poisson distribution with parameter λ=10

P(X=4)=

{e-λ*λx/x!} =

0.018917

if using excel use commannd :poisson(4,10,false)

2)

P(X=10)=

{e-λ*λx/x!} =

0.125110

if using excel use commannd :poisson(10,10,false)

3)

P(X=12)=

{e-λ*λx/x!} =

0.094780

if using excel use commannd :poisson(12,10,false)

4)

P(X<8)=

∑x=0x   {e-λ*λx/x!} =

0.2202

if using excel use commannd :poisson(7,10,true)

5)

for two months expected failure =2*10 =20

P(X=16)=

{e-λ*λx/x!} =

0.064561

if using excel use commannd :poisson(16,20,false)