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The Cardinal Machining Company manufactures nails. The quality control department randomly collects 75 nails from the production line and measures their length. these 75 nails had an average length of 2.938 inches with a variance of 0.155 inches square. Assume the nail length are normallly distributed. a) Consturct the appropiate 95% nfidence interval to determine if it is believable the mean length of Cardinal Machining Company nails is more tn 2.90 inches. b) Using the confidence interval found in part A, can the Cardinal Machining Company conclude the mean length of its nails is more than 2.90 inches? c) Is it believable that the standard deviation of nail lenghts is less than 0.45 inches? Conduct the appropiate hyothesis test using α = 0.01. d) Using your part C hypothesis test, can the Cardinal Machining Company conclude the standard deviation of nail lenghts is less than 0.45 inches at α = 0.01?

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