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.) IA 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? l:l (b) What is the (approximate) probability that the sample mean hardness for a random sample of 35 pins is at least 51? Z You may need to use the appropriate table in the Appendix of Tables to answer this question. Time taken by a randomly selected applicant for a mortgage to ll out a certain form has a normal distribution with mean value 9 min and standard deviation 3 min. If ve individuals ll out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Round your answer to four decimal places.) E You may need to use the appropriate table in the Appendix of Tables to answer this