Determine z, for the following of a. (Round your answers to two decimal places.) LA USE SALT (a) a = 0.0056 (b) a = 0.11 (c) a = 0.708 You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read ItYoung's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117-134)). (a) If X is the sample mean Young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa OX = GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = GPa OX = GPa (c) For which of the two random samples, the one of part (a) or the one of part (b), is * more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of X that comes with a smaller sample size. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of X that comes with a smaller sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of X that comes with a larger sample size. Need Help? Read ItThere are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.) LA USE SALT (a) If grading times are independent and the instructor begins grading at 6:50 PM. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 PM. TV news begins? (b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Watch ItRockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.5. (Round your answers to four decimal places.) LA USE SALT (a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51? (b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read ItSuppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.66 and standard deviation 0.72. LA USE SALT (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.007 Between 2.66 and 3.007 (Round your answers to four decimal places.) at most 3.00 between 2.66 and 3.00 (b) How large a sample size would be required to ensure that the first probability in part (a) is at least 0.997 (Round your answer up to the nearest whole number.) specimens You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Watch It
