1. A company was experiencing a chronic weld defect problem with a water outlet tube assembly. Each assembly manufactured is tested in a water tank. Data is collected on the gap x between the flange and pipe for 6 assemblies that leaked: 0.290 0.104 0.207 0.145 0.104 0.124
(a) Calculate the mean x manually using the formula and a calculator
(b) Calculate the sample standard deviation s manually using the formula and a calculator (M&F 2.32)
2. Ten bolted timber joints were tested using a 1/2 in. bolt placed in double shear through three pieces of 2 by 4 in. (nominal size) Douglas fir. The results of the shear tests were (loads shown in pounds):
specimen | load y1 at 1/16" | load y2 at 1/8" | ultimate load x
1 | 3500 | 3900 | 4000
2 | 3400 | 3500 | 3500
3 | 3100 | 3600 | 3800
4 | 2700 | 3500 | 4150
5 | 2900 | 3680 | 4050
6 | 3400 | 4250 | 4500
7 | 2700 | 3500 | 4400
8 | 3100 | 3700 | 4250
9 | 3100 | 4100 | 4550
10 | 2300 | 3200 | 3650
(a) Using a spreadsheet program, calculate the sample standard deviations and coefficients of variation for each set of data (ie load at 1/16", load at 1/8", ultimate load).
(b) Plot scatter diagrams and compute the sample correlation coefficients between the ultimate load x and each of the loads y1 and y2 at 1/16 and 1/8" deflection. Treat the ultimate load as the x variable and the loads at 1/16 and 1/8" as two y-variables. Calculate the correlation coefficients using both the built-in function as well as the equation for the correlation.
(c) Do you think that it is possible to use either of the simpler nondestructive tests as a predictive tool for the ultimate joint capacity? Of the two tests at 1/16 and 1/8", which is better as a predictor of the ultimate load? (B&C 1.2)
3. In a small geology class, each of the 4 students must write a report on one of 8 field trips. In how many different ways can they each chose one of the field trips if:
(a) no 2 students may choose the same field trip
(b) there are no restrictions on their choice? (M&F 3.19)
4. A carton of 12 rechargeable batteries contains one which is defective. An inspector randomly tests 3 batteries. What is the probability that the inspector will find the defective battery after 3 tries? (M&F 3.25)
5. When we roll a pair of balanced dice, what are the probabilities of getting the two dice to add up to:
(a) 7; (b) 11; (c) 7 or 11; (d) 3; (e) 2 or 12; (f) 2, 3 or 12 (M&F 3.29)