In pulse-amplitude modulation (PAM), a PAM word consists of a sequence of pulses, where each pulse may take on a given number of amplitude levels. Suppose a PAM word is n pulses long and each pulse may take on m different levels. (a) How many distinct PAM words are there? (b) If each PAM word, 4 pulses long, is equally likely to occur and each pulse can have one of three levels, (0, 1, 2}, what is the probability of a PAM word occurring with exactly two pulses of level 2?
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- Suppose each of 1000 players face a challenge in which a Bernoulli trial is repeated until the first success, that each attempt is independent of the others, and the chance of success on each attempt is p = 1/1000To the nearest whole number, how many of the 1000 players will achieve the first success within 1000 attempts, on average? THE ANSWER IS NOT 1, 500 OR 100010.18. A production process employs five machines in its three travel operations. A random sample of 164 failures was classified according to the machine and the shifting operation in which the failure occurred, and the results are shown in Table 10.6. Based on this information, is there any reason to doubt about the independence between the shifting operation and the machine failure? Use α = 0.01.A group of Sports Science students (n = 20) are selected from the population to investigate whether a 12-week plyometric-training programmed improves their standing long jump performance. In order to test whether this training improves performance, the students are tested for their long jump performance before they undertake a plyometric-training programme and then again at the end of the programmed .The following table present the results of before and after the training programmed. Test the claim that their long jump performance is higher after the training. Student Number (Before the training) Jump1 (After the training) Jump2 1 2.25 2.24 2 2.42 2.48 3 2.26 2.29 4 2.58 2.62 5 2.62 2.64 6 2.16 2.18 7 2.40 2.44 8 2.62 2.67 9 2.35 2.39 10 2.44 2.47 Follow the steps in hypothesis testing. Answer the following. What is the appropriate statistical test to use?…
- Marine biologists have noticed that the color of the outermost growth band on a clam tends to be related to the time of year in which the clam dies. A biologist conducted a small investigation of whether this is true for the species Protothaca staminea. She collected a sample of 55 clam shells in February and 55 clam shells in March. 14 of the shells from February had a dark color on the outermost growth band, whereas 8 of the shells from March had a dark color on the outermost growth band. Carry out a hypothesis test to see if there is a difference in the proportion of shells with a dark outermost growth band between the two months; specifically, if the population proportion in February is higher than March. Let ? = 0.1.Note: Do all calculations as February - MarchA) The point estimate for the true difference in proportion of dark growth bands between February and March is: Note: answer using 4 decimal precisionB) The test statistic, ztest, is: Note: answer using 2 decimal…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…According to the Bureau of Transportation Statistics, on-time performance by the airlines is described as follows: Action % of Time On time 70.8 National Aviation System delay 8.2 Aircraft arriving late 9.0 Other (because of weather and other conditions) 12.0 Records of 200 randomly selected flights for a major airline company showed that 125 planes were on time; 40 were delayed because of weather, 10 because of a National Aviation System delay, and the rest because of arriving late. At α = 0.05, do these results differ from the government’s statistics?
- 1. A University Director wants to see whether the average time (in minutes) it takesstudents to reach classes on time is different for three groups. The data are shown here.Junior Senior Graduates35 9 1518 3 627 12 2724 6 2221 12 2414821a) At α=0.05, can the owner conclude that there is a significant difference among themeans?b) If there is a significant difference among the means, test each pair of means?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 σ^2. e. If the store currently has in stock 10 chain-driven models and 8 shaft-driven models, what is theprobability that at least 7 out of the 15 customers select a chain-driven model from this stock? Please solve all and explain.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 σ^2. e. If the store currently has in stock 10 chain-driven models and 8 shaft-driven models, what is theprobability that at least 7 out of the 15 customers select a chain-driven model from this stock? Please help with parts a, b, and c.