A factory produces light bulbs with a 2% defect rate. If a random sample of 100 light bulbs is chosen, what is the probability of finding exactly 3 defective bulbs?
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- 13 percent of the patients in a study reported previous episodes of a stroke. Use 13 percent as the estimate of the prevalence of stroke within the population. If 70 subjects are chosen at random from the population, what is the probability that 10 percent of less would report an incidence of stroke?A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 43 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 4000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)It is known that 70% of adult workers have a high school diploma. If a random sample of 25 adult workers is selected, what is the expected number of them that would have a high school diploma?
- Assuming that the population is half male and half female, what is the probability that a random group of 11 people will contain 5 or more males?A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 51 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?Suppose that at a large university 30% of students are involved in intramural sports. If we randomly select 15 students from this university, what is the probability that fewer than 5 of these students are involved in intramural sports?
- Suppose that at a large university 30% of students are involved in intramural sports. If we randomly select 12 students from this university, what is the probability that fewer than 6 of these students are involved in intramural sports?Find the expected number of infected ducks in a sample of 5 ducks if the probability of an infected duck is 0.3 and the ducks can be considered independent.The records of an Italian shoe manufacturer show that 10% of shoes made are defective. Assuming independence, find the probability of getting 2 defective shoes in a batch of 12.
- A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 47 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)27.4% of males and 22.8% of females never eat breakfast. Suppose that random samples of 200 men and 200 women are drawn. What is the probability that no more than 108 of these 400 people never eat breakfast?A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect. The process improvement team agrees that the sample contains 27 bad items and 153 good items. The team gives the items to a “certified” operator for inspection. The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly. What is the probability that the inspector will reject an item? P(inspector will reject an item) = ________%. Enter value using one decimal place.
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