a retail store has implemented procedures aimed at reducing the number of bad ch

Question

a retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The stores's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 18 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 will meet its goal during a particular week. (b) find the probability that the store will not meet its goal during a particular week. (c) find the probability that the stores cashiers will cash no more than 10 bad checks per two week period. (d) find the probability that the store will cash no more than five bad checks per three week period. a retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The stores's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 18 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 will meet its goal during a particular week. (b) find the probability that the store will not meet its goal during a particular week. (c) find the probability that the stores cashiers will cash no more than 10 bad checks per two week period. (d) find the probability that the store will cash no more than five bad checks per three week period. a retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The stores's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 18 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 will meet its goal during a particular week. (b) find the probability that the store will not meet its goal during a particular week. (c) find the probability that the stores cashiers will cash no more than 10 bad checks per two week period. (d) find the probability that the store will cash no more than five bad checks per three week period. a retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The stores's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is 18 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 will meet its goal during a particular week. (b) find the probability that the store will not meet its goal during a particular week. (c) find the probability that the stores cashiers will cash no more than 10 bad checks per two week period. (d) find the probability that the store will cash no more than five bad checks per three week period.

Explanation / Answer

Solution:-

(A) The probability that the store will meet its goal during a particular week is 0.0071.

= 18

x = 8

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x < 8) = 0.0071

(b) The probability that the store will not meet its goal during a particular week is 0.9929.

= 18

x = 8

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x > 8) = 0.9929

(c) The probability that the stores cashiers will cash no more than 10 bad checks per two week period is  3.19 × 10-7.

Expected number of bad cash in two weeks = = 18 × 2 = 36

x = 10

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x < 10) = 3.19 × 10-7

(d) The probability that the store will cash no more than five bad checks per three week period is 1.5 × 10-17

Expected number of bad cash in three weeks = = 18 × 2 = 54

x = 5

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x < 5) = 1.5 × 10-17

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