Question 1 A previous survey shows that a machine making plastic components is correctly set up for the day's production on 95% of days. On days when it is set up correctly, 98% of the components produced are good. If the machine is not set up correctly, only 40% of the components produced are good. On a particular day, the machine is set up and the first component produced is found to be good. What is the probability that the machine is set up correctly?

Question 2 A wheel bearing factory rejects bearings if they are either oversize or undersize. The probability that a bearing is oversize is 0.004 while the probability that it is undersize is 0.01. (a) Are oversize rejection and undersize rejection events mutually exclusive? (b) What is the probability that a bearing selected at random is not within size limits? (c) What is the probability that a bearing selected at random is correctly sized?

Question 3 In Question 2, bearings are rejected if they are outside size limits. Incorrectly sized bearings are placed in a bin. If a bearing is selected at random from the rejects bin, what is the probability that it is undersize?

Question 4 A company manufacturing disk drives has two production plants located in Singapore and China. The Singapore plant contributes 30% of output with the balance coming from China. Over a prolonged period, it is observed that 4% of the Singapore drives are faulty while 5% of the Chinese produced drives are faulty. All drives are returned to the company's headquarters in Dublin for testing and dispatch. What is the probability that a drive found faulty at this check comes from China?

Question 5 A TV game show involves picking a coloured ball from one of two boxes. A blindfolded contestant chooses a box and then picks a ball at random from the box. Box 1 contains 2 green balls and seven red balls. Box 2 contains 4 green and 3 red balls. If a contestant picks a red ball, what is the probability that the contestant chose from Box 1?

Question 6 Show, with detailed working, how to find the mean, mode, median, interquartile range and standard deviation for the following set of data: {29, 41, 6, 9, 32, 22, 40, 36}