Question

A retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 12 per week. Let x denote the number of bad checks cashed per week. Assuming that x has a Poisson distribution:

(a) Find the probability that the store's cashiers will not cash any bad checks in a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(b) Find the probability that the store will meet its goal during a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(c) Find the probability that the store will not meet its goal during a particular week. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(d) Find the probability that the store's cashiers will cash no more than 10 bad checks per two-week period. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

(e) Find the probability that the store's cashiers will cash no more than five bad checks per three-week period. (Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

Answer 1

a) for expected number  of bad checks cashed per week =12=

hence probability that the store's cashiers will not cash any bad checks in a particular week=P(X=0)=

=0.0000

b)probability that the store will meet its goal during a particular week =P(no more then 8 bad cash checked)

= =0.1550

c)

  probability that the store will not meet its goal during a particular week =1-0.1550 =0.8450

d)

for two weeks ; expected number  of bad checks cashed =2*12 =24=

hence

probability that the store's cashiers will cash no more than ten bad checks per two-week period

=P(X<=10)= =0.0011

e)

for three weeks ; expected number  of bad checks cashed =3*12 =36=

probability that the store's cashiers will cash no more than five bad checks per three-week period

= =0.0000

please revert for any clarification required,