Kontakt Ltd. are a company that specialise in making waterproof switches. As part of their quality control procedures, 10 switches are selected at random from the switches produced each day and manually tested for defects. There is a 10% chance of an inspected switch having a defect. The table below shows the number of days 0, 1, ..., 10 defects occurred in the samples over the past 100 days. Number of defects Number of days

0 41

1 35

2 18

3 5

4 0

5 1

6 0

7 0

8 0

9 0

10 0

(a) Which probability distribution would you use to describe the number of defective switches in a sample of 10 switches? Clearly state any assumptions you must make.

(b) Carry out an appropriate test at the 5% significance level to determine if the distribution you identified in part (a) is consistent with the observed data.

(c) In the current process, quality control only monitors the defect rate of switches. That means 10% of switches sold by the company are defective. The company are upgrading their manufacturing processes to include automated defect checking to reduce the number of defective switches sold. Only switches that pass the automated defect checking process will be sold. However, the automated process is imperfect with only 95% of defective switches being correctly identified as defective. In addition, 7% of non-defective switches are incorrectly identified as defective. What is the probability that a switch sold by the company is defective?