Question: 1. 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
| 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 19 per week. Letxdenote the number of bad checks cashed per week. Assuming thatxhas 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.) |
| Probability |
| (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.) |
| Probability |
| (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.) |
| Probability |
| (d) | Find the probability that the store's cashiers will cash no more than ten bad checks per two-week period.(Round your answer to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) |
| Probability |
| (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.) |
| Probability |
| The customer service department for a wholesale electronics outlet claims that 75 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 18 customers who have filed complaints is selected. |
| (b) | Find each of the following if we assume that the claim is true:(Do not round intermediate calculations. Round final answers to 4 decimal places.) |
| 1. | P(x 13) | |
| 2. | P(x> 10) | |
| 3. | P(x 14) | |
| 4. | P(9 x 12) | |
| 5. | P(x 9) |
| (c) | Suppose that of the 18 customers selected, 9 have had their complaints resolved satisfactorily. Using partb, do you believe the claim of 75 percent satisfaction? Explain. |
| (Click to select)NoYes ; if the claim is true, thenP(x 9) is very (Click to select)smalllarge. |
| An industry representative claims that 27 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners. |
| (a) | Suppose that the representative's claim is true, and suppose that a sample of 4 dish owners is randomly selected. Assuming independence, use an appropriate formula to compute.(Do not round your intermediate calculation andround your answers to 4 decimal places.) |
| 1. | The probability that none of the dish owners in the sample subscribes to at least one premium movie channel. |
| Probability |
| 2. | The probability that more than two dish owners in the sample subscribe to at least one premium movie channel. |
| Probability |
| (b) | Suppose that the representative's claim is true, and suppose that a sample of 20 dish owners is randomly selected. Assuming independence, what is the probability that:(Do not round your intermediate calculation andround your answers to 4 decimal places.) |
| 1. | Nine or fewer dish owners in the sample subscribe to at least one premium movie channel? |
| Probability |
| 2. | More than 11 dish owners in the sample subscribe to at least one premium movie channel? |
| Probability |
| 3. | Fewer than five dish owners in the sample subscribe to at least one premium movie channel? |
| Probability |
| (c) | Suppose that, when we survey 20 randomly selected dish owners, we find that 4 of the dish owners actually subscribe to at least one premium movie channel. Using a probability you found in this exercise as the basis for your answer, do you believe the industry representative's claim? Explain. |
| (Click to select)YesNo ; if the claim is true, then the probability of fewer than 5 is very (Click to select)smalllarge. |
| A candy company claims that its new chocolate almond bar averages 12 almonds per bar. Letxdenote the number of almonds in the next bar that you buy. Use the Poisson distribution to findP(x 4) if the candy company's claim is correct. Ifxactually turns out to be 4, what do you think of the claim?(Leave no cells blank - be certain to enter "0" wherever required. Round your answer to 4 decimal places.) |
| P(x 4) |
| The claim is (Click to select)probably notprobablytrue. |
| 36 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. |
| (1) | Use the binomial formula to calculate the probability that exactly five customers make a purchase.(Round your answer to 4 decimal places.) |
| Probability |
| (2) | Use the binomial formula to calculate the probability that at least three customers make a purchase.(Round your answer to 4 decimal places.) |
| Probability |
| (3) | Use the binomial formula to calculate the probability that two or fewer customers make a purchase.(Round your answer to 4 decimal places.) |
| Probability |
| (4) | Use the binomial formula to calculate the probability that at least one customer makes a purchase.(Round your answer to 4 decimal places.) |
| Probability |
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