Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1. (Round your answers to four decimal...

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(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 12 pins is at least 51?

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?