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Rockwell 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.) In USE SALT (a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 18 pins is at least 51? .35 X (b) What is the (approximate) probability that the sample mean hardness for a random sample of 35 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 It [-/2 Points] DETAILS DEVORESTAT9 5.E.054.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.68 and standard deviation 0.81. 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 3.00? Between 2.68 and 3.00? (Round your answers to four decimal places.) at most 3.00 between 2.68 and 3.00 (b) How large a sample size would be required to ensure that the first probability in part (a) is at least 0.99? (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