A doctor has taken a vaccine from either storage unit P (which contains 30 current and 10 outdated vaccines), or from unit Q (which contains 20 current and 20 outdated vaccines), or from unit R (which contains 10 current and 30 outdated vaccines), but she is twice as likely to have taken it from unit P as from unit Q and twice as likely to have taken it from unit Q as from unit R.
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2In a certain city, only 2 newspapers A and B are published. It is known that 25% of the city population read A and 20% read B while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. What is the percentage of the population who read an advertisement?An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. Company A makes 80% of the ELTs, Company B makes 15% of them and Company C makes the other 5%. The ELTs made by Company A have a 7.8% rate of defects, the Company B ELTs have a 6.3% rate of defects and the Company C ELTs have 6.4% rate of defects. If a randomly selected ELT is tested and found to be defective, find is the probability that it was made by Company A? Give your answer to three decimal places.
- An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Altigauge Manufacturing Company makes 80% of the ELTS, the Bryant Company makes 15% of them, and the Chartair Company makes the other 5%. The ELTS made by Altigauge have a 4% rate of defects, the Bryant ELTS have a 6% rate of defects, and the Chartair ELTS have a 9% rate of defects (which helps to explain why Chartair has the lowest market share). i) If an ELT is randomly selected from the general population of all ELTS, find the probability that it was made by the Altigauge Manufacturing Company. If a randomly selected ELT is then tested and is found to be ii) defective, find the probability that it was made by the Altigauge Manufacturing Company.An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Altigauge Manufacturing Company makes 80% of the ELTS, the Bryant Company makes 15% of them, and the Chartair Company makes the other 5%. The ELTS made by Altigauge have a 4% rate of defects, the Bryant ELTS have a 6% rate of defects, and the Chartair ELTS have a 9% rate of defects (which helps to explain why Chartair has the lowest market share). a. If an ELT is randomly selected from the general population of all ELTS, find the probability that it was made by the Altigauge Manufacturing Company. b. If a randomly selected ELT is then tested and is found to be defective, find the probability that it was made by the Altigauge Manufacturing Company. c. What is the probablity that a randomly selected ELT is defective?In comparing the average protein content µ1 and µ2 of two brands of dog food, a consumer testing service finds that fifty 5-pund packages of brand A dog food had an average protein content x̅1=11 ounces per package and a s.d of s1 = 1 ounce, while sixty-5 pound packages of brand B dog food has an average protein content x̅2=9ounces per package and a s.d of s2 = 0.5 ounce. A difference of 0.5 ounces is considered to be not sufficiently important to report as a consumer issue. Therefore, a decision was made to test the hypothesis.
- It has been observed that some persons who suffer renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode? Select the [Alternative…A manufacturing company produces a widget that comes in two types which are A and B. 33% of the widgets produced are type A and 67% are type B. The widgets also come in three sizes. Not accounting for widget type, the company produces 20% of widgets in size 1, 45% of widgets in size 2, and 35% of widgets in size 3. If somebody pulls a widget for quality testing from the production facility, which is the probability that the widget is type A or size 2? Also the probability of any widget being both type A and size 2 is 0.16. Is the event of type A and the event of size 2 mutually exclusive or not?It has been observed that some persons who suffer renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 10% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.01, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Alternative…
- A researcher wonders if there an association between the incidence of colds and the amount of vitamin C taken. He recruits 98 volunteers and randomly assigns 29 of them to take 500 mg of vitamin C, 17 of them to take 1000 mg of vitamin C and the rest to take no vitamin C. At the end of the study, it was determined that 28 of the volunteers did not have any colds where 12 of them were in the 500 mg group and 8 of them were in the 1000 mg group. Test the appropriate hypothesis at α=.01 Complete the table of expected counts under the null hypothesis. At least one cold No colds No vitamin C 14.857 500 mg vitamin C 20.714 1000 mg vitamin C 12.143 4.857It has been observed that some persons who suffer renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 45 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 12% of the first group has a second episode and 14% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is less than the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region,…Avobenzone is one of the active ingredients in several commercially available sunscreens. It can be absorbed into the bloodstream when sunscreen is applied to the skin. The Food and Drug Administration has expressed concern about the safety of absorbing too much avobenzone. Researchers recruited 24 healthy volunteers to investigate avobenzone absorption for four different commercially available sunscreens: two sprays, a lotion, and a cream. Do the types of sunscreens (spray, lotion, and cream) differ in terms of how much avobenzone is absorbed into the blood? Subjects were randomly assigned to one of the four sunscreens, with six subjects for each. Subjects had 2 milligrams of sunscreen per 1 cm? applied to 75% of their body surface area (area outside of normal swimwear) four times per day for four days. The amount of avobenzone absorbed into the bloodstream (in nanograms per milliliter ap-plied, ng/mL) after 150 hours was then measured for each subject. For the purpose of analyzing…
