Can someone help me out with these 4 word problems and explain a bit? Thanks
A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 47.3, with a standard deviation of 10.0. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year. a) According to Chebyshev's theorem, at least (Choose one) |of the X ? scores lie between 27.3 and 67.3 b) According to Chebyshev's theorem, at least - (about 89%) of the scores lie between ] and ]. (Round your answer to 1 decimal place.) A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.1 ounces of coffee per cup. BIG has good reason to believe that the mean amount of coffee dispensed by the machine, J, is less than 7.1 ounces, and plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 6.6 ounces and that the standard deviation is 0.3 ounces. Based on this information, complete the parts below. (a) What are the null hypothesis Ho and the alternative hypothesis H, that should be used for the test? X H :D O0 020 0-0 0*0 (b) Suppose that BIG decides to reject the null hypothesis. What sort of error might it be making? (Choose one) x 2 (c) Suppose the true mean amount of coffee disper chine is 6.4 ounces. Fill in the blanks to describe a Type II error. A Type II error would be (Choose one) v the hypothesis that u is [(Choose one) (Choose one) when, in fact, u is (Choose one) A researcher believes that about 74% of the seeds planted with the aid of a new chemical fertilizer will germinate. He chooses a random sample of 135 seeds and plants them with the aid of the fertilizer. Assuming his belief to be true, approximate the probability that more than 99 of the 135 seeds will germinate. Us the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. If necessary, consult a list of formulas.) X ? For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 520 and a standard deviation of 175. The grading process of this year's exam has just begun. The average score of the 35 exams graded so far is 524. What is the probability that a sample of 35 exams will have a mean score of 524 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places
