a) A battery manufacturer was interested in predicting the annual maintenance cost of the battery…
a) A battery manufacturer was interested in predicting the annual maintenance cost of the battery manufacturing machines based upon the age of the machine. A sample of ten machines revealed the following ages and maintenance costs during the previous year.
|
Age years) |
9 |
4 |
2 |
8 |
4 |
5 |
1 |
3 |
6 |
8 |
|
cost |
40 |
12 |
8 |
27 |
15 |
17 |
5 |
10 |
25 |
31 |
i. Define regression analysis [1 Mark ]ii. Fit the linear regression model to the data using the least squares method.
[7 Marks]
iii. Interpret the meaning of the slope in the linear regression model in part ( ii )
[1 Mark ]
iv. Predict the maintenance cost of a machine that is 10 years old. [1 Mark]
b) An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of a crash. The Ultimate manufacturing company makes 80% of the ELTs, the Bryant Company makes 15% of them, and the Charter air company makes the other 5%. The ELTs made by Ultimate have a 4% rate of defects; the Bryant ELTs have a 6% rate of defects, and the Charter air ELTs have 9% rate of defect (Which helps to explain why charterair has the lowest market share). An ELT is randomly selected from the general population of all ELTs then tested and is found to be defective.
i) Find the probability that the ELT is defective. [4 Marks]ii) If a randomly selected ELT is defective, find the probability that it was made by the ultimate manufacturing company [3 Marks]iii) If a randomly selected ELT is defective, find the probability that it was made by the charterair manufacturing company. [3 Marks]
