QUESTION 1 25 points Save Opportunity Knocks is a top manufacturer of exterior doors. They are conducting a study of their top selling door, which is designed to be 72 inches tall, but actual heights of the doors are normally distributed (parameters unknown). The QC department randomly collects 71 doors and measures their heights. These 71 doors were found to have an average height of 72.13 inches with a standard deviation of 0.47 inches. a. Is it believable that the standard deviation of the heights of the doors is more than 0.50 inches. Conduct the appropriate hypothesis test using a = 0.05. b. Is it believable the mean height of the doors is 72.0 inches? Construct the appropriate 99% confidence interval c. Of the 71 doors tested, 6 are found to be defective. Opportunity Knocks is very concerned at the possibility of selling defective items. Is it believable that the proportion of defective doors is less than 10%? Construct the appropriate 90% confidence interval. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac)