The lengths of lumber a machine cuts are normally distributed with a mean of 90 inches and a standard deviation of 0.3 inch.(a) What is the probability that a randomly selected board cut by the machine has a length greater than 90.09 inches?(b) A sample of 42 boards is randomly selected. What is the probability that their mean length is greater than 90.09 inches?
(a) The probability of board being longer than 90.09 is about 38%.
(b) The probability of a sample (n=42) having a mean length of 90.09 is about 2.6%
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