The average teacher's salary in a certain state is $37,764. Assume a normal distribution with o=$5100. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator and round the answers at least four decimal places. (a) What is the probability that a randomly selected teacher's salary is greater than $41,000? P(X 41,000) #3 (b) For a sample of 75 teachers, what is the probability that the sample mean is greater than $38.300? PX38,300)

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