3. A local council is considering purchasing a snow plough which could cost $20,000 per annum. This would save on outside contractors but the amount would depend on the severity of the winter weather

(a)  

4. A new product is expected to generate the following profits or losses:

(a)  

7. A baker produces four flavours of their best-selling cupcake (chocolate, vanilla, lemon and strawberry) in equal quantities. For quality checking purposes, one cake is selected from each batch of 100 cakes produced.What is the probability that the cake selected is chocolate flavoured?

(a)  

11. The weights of a certain mass produced item are known, over a long period of time, to be normally distributed with a mean of 8kg and a standard deviation of 0.02kg.If items whose weights lie outside the range 7.985 - 8.035kg are deemed to be faulty, what percentage of products will be faulty (to two decimal places)?

(a)  

13. A soft drink manufacturer bottles its products in 500 ml bottles. A review of one of the bottling machines showed that the mean amount in each bottle is 498ml, with a standard deviation of 0.9ml.Adopting a normal distribution, what percentage of containers will contain more than the notional contents of 500ml (to 2 decimal places)?

(a)  

14. A business has analysed its customer collection data and has found that a customer takes 37 days to pay on average with a standard deviation of 4 days.Assuming the data follows a normal distribution, what is the probability that a customer will take longer than 47 days to pay (to 2 decimal places)?

(a)