Bob Bailey is a local factory owner. Among other things, he manufactures bolts of various sizes to be used in construction projects. He has been studying his machines, and is interested in the answer to several questions. 1. Due to heavy use of the machines used in the manufacturing process, there are inevitable breakdowns. Based on years of data on past breakdowns, Bob has determined that the repair time follows a uniform distribution over 4 to 12 hours. (a) Describe this distribution (What is the height of the density curve?, On average, what is the repair time?, What is a typical deviation from the average repair time?) (b) If a random machine has a breakdown this morning, what is the probability that the repair can be done in less than 6 hours? (c) If a random machine has a breakdown this morning, what is the probability that the repair will take between 6 and 9 hours? 2. One of the machine produces a 2 inch bolt. Based on years of measurements, Bob knows that the lengths of the bolts follow a normal distribution with a mean of 2 inches and a standard deviation of .12 inch. (a) What is the probability that a randomly selected bolt will be longer than 2.1 inches? (b) What is the probability that a randomly selected bolt will be between 1.95 and 2.2 inches? (c) Another machine automatically sorts the bolts shortest to longest. At the end of the day yesterday, about 10% of the bolts had to be tossed out because they were too short. How short were they? (d) To check that the machine is properly calibrated, a random sample of 6 bolts are taken each day and their mean length is calculated. i. What is the probability that the average lengths of these bolts will be longer than 2.1 inches? ii. What is the probability that the average lengths of these bolts will be between 1.95 and 2.2 inches? iii. If the average length of these bolts falls into the bottom 10% of all such averages, the machine might need to be recalibrated. What average length is the criteria we are checking against? (e) All of the answers in part 2d are different from the answers in part 2 (a)-(c). Bob does not understand statistics, so he needs you to explain why this is. 3. Another machine manufactures a 5 inch bolt. Each day, six sample bolts are pulled from the production line and measured for accuracy. The data is located in the file BobsBolts.xls located in Bb. Each row represents one day. Use this file (and StatCrunch as necessary) to answer the following questions. (a) The first questions is to determine if the range is in control. Create the appropriate chart to determine this. Describe the important features of the chart and determine if the range appears to be in control. (b) If the range is in control, the next question would be whether or not the mean is in control. Create the appropriate chart to determine this. Describe the important features of the chart and determine if the mean appears to be in control.