Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.
a. If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51?
b. Without assuming population normality, what is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51?
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