What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
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A biomedical research company produces 44%44% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 0.9%0.9% of the insulin produced at the plant in Kansas City is defective, while 0.85%0.85% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
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- A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 63.8%. What is the probability that in a random sample of 440 headache sufferers, less than 59.7% obtain reliefA biomedical research company produces 40% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 0.75% of the insulin produced at the plant in Kansas City is defective, while 0.5% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 927 peas, with 723 of them having red flowers. If we assume, as the scientist did, that under these circumstances, there is a 3/4 probability that a pea will have a red flower, we would expect that 695.25 (or about 695) of the peas would have red flowers, so the result of 723 peas with red flowers is more than expected. a. If the scientist's assumed probability is correct, find the probability of getting 723 or more peas with red flowers. b. Is 723 peas with red flowers significantly high? c. What do these results suggest about the scientist's assumption that 3/4 of peas will have red flowers?
- An airline is considering adding a route to the city of Buffalo, NY. Market research predicts that if the airline serves Buffalo, there is a 32% probability of making a $500,000 profit, a 22% chance of breaking even, and a 46% probability of losing $300,000. What is the expected value of adding a route to Buffalo?Deer ticks can carry both Lyme disease and human granulocytic ehrlichiosis (HGE). In a study of ticks in the Midwest, it was found that 15 % carried Lyme disease, while 11 % carried HGE. In addition, of the ticks with either Lyme disease or HGE, 16 % carried both diseases. (a) What is the probability P[L H] that a tick carrries both Lyme disease (L) and HGE (H)? P[LH] = (b) What is the conditional probability that a tick carries HGE, given that it has Lyme disease? P[H|L] =The Watts New Lightbulb Corporation ships large consignments of lightbulbs to big industrial users. When the production process is functioning correctly, which is 90% of the time, 10% of all bulbs produced are defective. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 50%. If a defective bulb is found, what is the probability that the process is functioning correctly? If a nondefective bulb is found, what is the probability that the process is operating correctly?
- A biomedical research company produces 45%45% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 0.85%0.85% of the insulin produced at the plant in Kansas City is defective, while 0.75%0.75% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?A report to Health Canada indicated that an intensive education program was used in an attempt to lower the rate of lung cancer development among females. After running the program, a long-term follow-up study of 40a females was conducted, which revealed the current rate of lung cancer development is 7.a %. (a=1) Find the probability that 10 or less females have lung cancer development.Bicycles for hire at the Durban Beach front are deemed beyond repair when one or both itswheels are damaged. According to current statistics, there is an 8% chance that the front wheelgets damaged and a 12% chance the back wheel gets damaged.What is the probability that a hired bike will be deemed beyond repair, provided that the wheelsget damaged independently of each other?
- An electronics firm claims that the proportion of defective units from a certain process is 5%. A buyer has a standard procedure of inspecting 16 units selected randomly from a large lot. On a particular occasion, the buyer found 6 items defective. What is the probability of having 6 or more defective items, given that the claim of 5% defective is correct?Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results. What do you conclude? The probability shows that the sample results ▼ could could not have easily occurred by chance. It appears that there ▼ is is not sufficient evidence to conclude that seatbelts do have an effect on survival rate.
