Question

8. You are given two boxes, one contains nuts and the other contains bolts. Below is a picture of a bolt. The D indicates Below right is a side and overhead picture of a nut. The the diameter of the bolt D indicates the diameter of the hole INSIDE the nut. ATI RODI c ISO METRIC AND WASHERS A bolt is supposed to fit inside a nut. On the right is a picture of a bolt properly fitting inside a nut. The diameters of the bolts are approximately normally distributed with mean 2 centimeters (cm) and standard deviation 0.03 cm. The diameters of the holes in the nuts are approximately normally distributed with mean 2.02 cm and standard deviation 0.04 cm. Suppose you randomly choose a bolt from the box of bolts, and a nut from the box of nuts. A bolt and a nut will fit together if (1) the diameter of the hole in the nut is greater than the diameter of the hole in the bolt AND (2) the difference between the diameters is not greater than 0.05 centimeters. a) (3 pts) First, define random variables corresponding to the diameter of a randomly chosen bolt and to the diameter of the hole of a randomly chosen nut. Also, give the distributions (names and parameters) of these random variables. b) (3 pts) Second, let D be the difference in the diameters of the randomly chosen bolt and the randomly chosen nut. Write a formula for D in terms of the random variables from part 7a. c) (5 pts) Third, Handout" find the distribution ofD .CLEARLY TELL ME which property or properties you use from that sheet. * Show the work done with said property or properties to find the distribution. * Give the name of the distribution and its parameters. d) (5 pts) Finally, find the probability that the nut and the bolt will fit together

Answer 1