8. Suppose that a class contains 10 boys and 15 girls, and suppose that eight students are to be selected at random from the class without replacement. Let X denote the number of boys that are selected, and let Y denote the number of girls that are selected. Find E(X – Y). -
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- Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. Solve for P(X=2).Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…Suppose a finite population has 6 items and 2 items are selected at random without replacement, then all possible samples will be: a. 6b. 15c. 2d. 12 e. 36
- A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) fY|2 4) E(x)Show all workA manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Determine the following. 1) fxy(x,y) 2) fx (x)3) E(x)4) E(Y|X=2)5) V(Y|X=2)6) Are X and Y independent? Why?Suppose that Fred, a United States politician from a large western state, wants to create a new law that would require children under the age of 16 to be accompanied by an adult at all times in public places. Based on previous voting records, Fred believes that he could gain the support of 2525% of likely voters. To test his hypothesis, Fred conducts a random survey of 12001200 likely voters and asks if they would support his proposition. Let ?X denote the number of likely voters in Fred's sample that pledge their support, assuming that Fred's belief that 25%25% of likely voters would support his proposal. Which of the following statements are true about the sampling distribution of ?X? -The sampling distribution of ?X is approximately binomial with ?=1200n=1200 and ?=0.25p=0.25. -The sampling distribution of ?X is exactly normal with ?=0.5μ=0.5 and ?=0.0125σ=0.0125. -The sampling distribution of ?X is exactly binomial with ?=1200n=1200 and ?=0.25p=0.25. -The sampling…
- they take samples of 4 fireworks for quality co from and examine them for defects. let X be the number of defective fireworks in the sample of 4.When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B a) Consider a random sample of n=9 people who donated blood over the past three months. The expected number of people with blood type O+ is and the expected number of people with blood type A- is Calculate the following probabilities: P(X=5)= __________ Round your answer to 4 decimal places. P(X>2)= __________ Round your answer to 4 decimal places. b) Consider a random sample of n=40 people who donated blood over the past three months. Use the relevant probability function of Y to calculate the probability that 2 people in the random sample will have type A- blood. ________…
- Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. a) Solve for P(x=0, y=0) b)Solve for P(x=1, y=2) c)Solve for P(x=2, y=1)From historical data at a local restaurant indicate that 60% of customers order coffee, 15% order soft drinks, and the remaining order water. The owner of the restaurant is planning on opening a new restaurant for the purpose of stocking enough of various drinks, wants to know if the proportions are the same for his new restaurant as they were for his original restaurant. In a sample of 1000 customers at the new restaurant, 550 ordered coffee, 190 order soft drinks, and the remaining simply wanted water. At the 5% level of significance, does it appear the proportions have changed?A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine V(Y|X=2).