2.1 Explain the meaning of the binomial probability distribution and state the conditions under which this distribution is used. (5)

2.2 A section supervisor of an insurance company records the lengths of time that his secretary spends having morning tea. He finds that the times are approximately normally distributed with a mean of 20 minutes and a standard deviation of 6 minutes. What is the probability that the time taken by the secretary is:

2.2.1 less than 10 minutes? (2)

2.2.2 more than 27 minutes? (2)

2.2.3 more than 15 minutes? (4)

2.2.4 between 10 minutes and 30 minutes? (5)

2.3 In a survey conducted by the Society for Human Resource Management, 68% of workers said that employers have the right to monitor their telephone use. Suppose that a random sample of 20 workers is selected and are asked if employers have the right to monitor telephone use. What is the probability that:

2.3.1 5 or less of the workers agree? (3)

2.3.2 15 or less of the workers agree?