Question

ristruct Question 9 Jof 9 1000 points A relail slore has inplemented procetures aimed al reducing the numter of bad checks cashed by is cashiers. The slore's goal is lo cash na mare than eigt bad checks per week. The average number ofad checks cashed is 14 per week Lel x cehe nber of bad checks week. Assuming that x has a Poisson disaiburtion (a) Find the probability tha: the store's cashiers wil not cash any bad checks in a particular week Round your answer to 4 decimal places. Leave no cells blank-be certain to enter" wherever required.) Probablity (b,-ind the prooability that the store will meat ts goal during a particular week. (Round your answer to 4 decimal places. Leave no ¢ells blank-be certain to enter "O" wherever required.) Probabilty (c) Fin tee gurcitsatnbty s tthe sle wil rt eeils geel duinhiruler wew Round your answer to 4 decimal places. Leave no cells blank-be certain to enter "o" wherever required. 1523 (d) Find the probability that the store's cashiers will cash no mcre than ten bad checks per two week period Round your answer to 4 decimal places. Leave no cells blank be certain to enter"" wherever required.) Probablity () Find the probablity tha the store's cashiers wil cash no more than tve bad checks per throo-wock penod. (Round your answer to 4 decimal places. Leave no cells blank be certain to enter"O" wherever required.) Prodablity References eBook & Resources Type here to search

Answer 1

$Let~X=no.~of~bad~checks~weeks\sim Poi(14).\\ (a)~P(X=0)=e^{-14}=0.0000\\ (b)~P(X\leq 8)=\sum_{x=0}^8\frac{e^{-14}(14)^x}{x!}=0.0621\\ (c)~P(X>8)=1-P(X\leq 8)=1-0.0621=0.9379\\ (d)~P(X\leq 10)=\sum_{x=0}^{10}\frac{e^{-14}(14)^x}{x!}=0.1757\\ (e)~Y=no.~of~bad~checks~3~weeks\sim Poi(42),\\ ~using~additive~property~of~Poisson~distribution\\ P(Y\leq 2)=\sum_{x=0}^{2}\frac{e^{-42}(42)^x}{x!}=0.0000$