Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.6. (Round your answers to four decimal places.)   (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? (b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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 1.6. (Round your answers to four decimal places.)

 
(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?


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