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1 A 95% confidence interval for the mean income of shop assistants in a certain city is found to be (£12,000, £15,000). Say in one sentence what this means. Would a 99% confidence interval be better than a 95% one? (Say why/why not.)

2. A charity believes that when it puts out an appeal for charitable donations the donations it receives will be normally distributed with a mean of £50 and a standard deviation of £6.
a) Find the probability that the first donation it receives will be less than £40.

b) Find the value x such that 5% of donations are more than £x.

3. A consultant for Dell was investigating computer usage among students at a particular university. 200 undergraduates and 100 postgraduates were chosen at random and asked if they owned a laptop. It was found that 81 of the undergraduates and 63 of the postgraduates owned a laptop. The consultant calculated that 48% (144 out of 300) of the students interviewed owned a laptop. Explain, with reasons, whether the figure of 48% will be a good estimate of the proportion of all students who own a laptop.

4. For a certain variable, the standard deviation in a large population is equal to 12.5. How big a sample is needed to be 95% sure that the sample mean is within 1.5 units of the population mean? (5 marks)