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1A.

Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is o = 9.9 milligrams. Juan repeats the measurement 6 times and records the mean x of his 6 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 6 measurements and averaging them, what would be the standard deviation of all his x's?) |mg. (b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 2.7 milligrams? Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement. O The average of several measurements will always have a greater standard deviation than the result of a single measurement. O The average of several measurements will always equal the true mean. O The average of several measurements is much more likely to be close to the true mean than a single measurement.The number of flaws per square yard in a type of carpet material varies with mean 1.71 flaws per square yard and standard deviation 1.24 flaws per square yard. The population distribution cannot be normal, because a count takes only whole-number values. An inspector studies 219 square yards of the material, records the number of flaws found in each square yard, and calculates x, the mean number of flaws per square yard inspected. Use the central limit theorem to find the approximate probability that the mean number of flaws exceeds 1.88 per square yard. (Round your answer to four decimal places.)Here is a simple probability model for multipleechoice tests. Suppose that a student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A good student has a higher ,0 than a poor student.) The correctness of an answer to any specic question doesn't depend on other questions. A test contains n questions. Then the proportion of Correct answers that a student gives is a sample proportion p from an SR5 of size n drawn from a population with population proportion p. (a) Julie is a good student for whom p : 0.71. Find the probability that Julie soores 69% or lower on a 105 question test. E (b) If the test contains 245 questions, what is the probability that Julie will score 69% or lower? (Use the normal approximation to the sampling distribution to solve this problem.) E (c) How many questions must the test contain in order to reduce the standard deviation of Julie's proportion of correct answers to oneefourth its value for an 1007item test? (Use the sampling approximation to the binomial distribution to solve this problem.) (d) Laura is a weaker student for whom p : 0.6. Does the answer you gave in (c) for the standard deviation of Julie's score apply to Laura's standard deviation also? Explain. O No, the number of questions would be greater: 0 Yes, the number of questions would be the same. 0 No, the number of questions would be smaller: Investors remember 1987 as the year stocks lost 20% of their value in a single day. For 1987 as a whole, the mean return of all common stocks on the New York Stock Exchange was 1.; = 72%. (That is, these stocks lost an average of 72%. of their value in 1987.) The standard deviation of returns was about U : 28%. (a) What are the mean and the standard deviation of the distribution of 4estock portfolios in 1987. \"at: (b) Assuming that the population distribution of returns on individual common stocks is normal, what is the prohab v that a randomly chosen stock showed a return of at least 8% in 1937? |:| (5) Assuming that the population distribution of returns on individual common stocks is normal, what is the probability that a randomly chosen portfolio of 5 stocks showed a return of at least 8% in 1957? |:| (d) What percentage of 7estock portfolios lost money in 1957'? The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 17 and standard deviation 4.7. (a) What is the probability that a single Student randomly chosen from all those taking the test scores 26 or higher? |:| (b) Now take an SR5 of 37 students who took the test. What are the mean and standard deviation of the average (sample mean) score for the 3? students? Do your results depend on the fact that individual scores have a normal distribution? 0 yes Ono (c) What is the probability that the mean score ; of these students is 18.59 or higher? |:|