Question: Problem 3: Assume that a device called a widget exists and is designed to output macs. Assume that the number of macs produced in a

in a single minute is approximated by Gaussian density function. You make

Problem 3: Assume that a device called a "widget" exists and is designed to output "macs". Assume that the number of macs produced in a single minute is approximated by Gaussian density function. You make observations for 30 minutes and find a sample mean (MN) of 12.5 macs/minute. (NOTE: each observation is one minute in duration) a) (6 points) Find the two-sided 98% confidence interval for the estimated sample mean assuming o = 0.5 macs/minute.c) (8 points) Find the two-sided 98% confidence interval for the estimated sample mean given above (with N=30), assuming you use the sample standard deviation of 0.55 macs/minute.b) (6 points) How many minutes should be observed so that the estimated sample mean is within +0.2 of the true mean with 98% confidence, assuming o = 0.5 macs/minute

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