Compute (a) ?(? = 1), (b) ?(? ≥ 4), and (c) ?(1 ≤ ? ≤ 3).
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2. Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of
a high-pitched oscillating noise when the refrigerator is running. Suppose that four of these 12 have
defective compressors and the other eight have less serious problems. If they are examined in random
order, let ? be the number among the first six examined that have a defective compressor. Compute (a)
?(? = 1), (b) ?(? ≥ 4), and (c) ?(1 ≤ ? ≤ 3).
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- 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)…Each of 13 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 10 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 9 examined that have a defective compressor. (a) Calculate P(X = 7) and P(X ≤ 7). (Round your answers to four decimal places.) (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normal
- 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. (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) P(X ≤ 3) than to use the hypergeometric pmf. We can approximate the…Each of 13 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 10 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 9 examined that have a defective compressor. ***Please solve both parts or do not attempt this problem.*** (a) Calculate P(X ≤ 7). (Round your answer to four decimal places.) (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)3. Each of a group of 20 intermediate tennis players is given two rackets, one having nylon strings and the other synthetic gut strings. After several weeks of playing with the two rackets, each player will be asked to state a preference for one of the two types of strings. Let p denote the proportion of all such players who would prefer gut to nylon, and let X be the number of players in the sample who prefer gut. Because gut strings are more expensive, consider the null hypothesis that at most 50% of all such players prefer gut. We simplify this to H0: p = .5, planning to reject H0 only if sample evidence strongly favors gut strings. (a) Is a significance level of exactly .05 achievable? If not, what is the largest α smaller than .05 that is achievable? (b) If 60% of all enthusiasts prefer gut, calculate the probability of a type II error using the significance level from part (a). Repeat if 80% of all enthusiasts prefer gut. (c) If 13 out of the 20 players prefer gut, should H0 be…
- A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 10 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.54 0.62 0.37 0.42 0.58 0.50 0.53 0.64 0.53 0.40 Brand 2 0.39 0.33 0.33 0.33 0.28 0.46 0.29 0.55 0.45 0.37 Difference(Brand 1 - Brand 2) 0.15 0.29 0.04 0.09 0.30 0.04 0.24…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…A manufacturer of “Keep it Warm” bags is interested in comparing the heat retention of bagswhen used at five different temperatures (100 oF, 125 oF, 150 oF, 175 oF, and 200 oF). Thirty bagsare selected randomly from last week’s production and randomly assigned, six each, to fivedifferent groups. Items from group 1 at beginning temperature 100 oF were kept in bags for anhour, and the temperatures of those items were recorded after an hour. Similarly, groups 2 to 5were assigned items at 125 oF, 150 oF, 175 oF, and 200 oF, respectively.a. Identify the type of study used here.b. What type of inference is possible from this study?
- Of all customers purchasing automatic garage door openers, 75% purchase chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model.a. What is the frequency function (pmf) of X?b. Compute P(X > 10).c. Compute P( 6 ≤ X ≤ 10).d. Compute µ and σ2e. If the store currently has in stock 10 chain-driven models and 8 shaft-driven models, what is the probability that at least 7 out of the 15 customers select a chain-driven model from this stock?Each of 12 refrigerators of a certain type has beenreturned to a distributor because of an audible, highpitched,oscillating noise when the refrigerators are running.Suppose that 7 of these refrigerators have a defectivecompressor 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 havea defective compressor.a. Calculate P(X 5 4) and P(X # 4)b. Determine the probability that X exceeds its meanvalue by more than 1 standard deviation.c. Consider a large shipment of 400 refrigerators, ofwhich 40 have defective compressors. If X is thenumber among 15 randomly selected refrigeratorsthat have defective compressors, describe a lesstedious way to calculate (at least approximately)P(X # 5) than to use the hypergeometric pmf.A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…