Normal Probability & Sampling Distribution of Sample Mean

CFL Manufacturing lists the average weight of parts produced as 425mg with a standard deviation of 3mg.

A. What is the probability that a single part will weigh 426mg or more? (assume the parts are relatively normally distributed)
B. A study of 36 parts finds an average weight of 426mg with a standard deviation of 3.098mg. identify the following: (on the attachment)
C. What is the probability that a sample mean weight of 36 parts will be more than 426mg?
D. What is the value of the standard error of the mean for part C above?

In one region, the April energy consumption data for all single family homes are found to be normally distributed with a mean of 1290 kilowatts and a standard deviation of 235 kw.

A. What is the probability that a single family home in that region used more than 1320 kw?
B. If 50 different homes were randomly selected, what is the value of the value of the standard error
C. For the sample of 50 different, randomly selected homes, find the probability that their mean energy consumption level for April was greater than 1320kw?
D. Compare the results for part A and part C and explain why the probabilities changed ( use the central limit theorum to explain your answer)

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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