4. A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.6 years. The life of a dishwasher is normally distributed. Suppose you are a manufacturer and you take a sample of 16 dishwashers that you made. a. Find the mean of the sample mean. b. Find the standard deviation of the sample mean. c. What is the shape of the distribution of the sample mean? Why? d. Construct and label a Sampling Distribution of Sample Means for this problem. e. Find the probability that the sample mean of the dishwashers is more than 10.5 years. f. If you found the sample mean life of the 10 dishwashers to be 7.2 years, would you have a concern with the manufacturing process? Why or why not?

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