1)The time taken to thoroughly audit the books of a small business by Royce, Smith and Jones Auditors has been found to follow a normal distribution with a mean of 5.8 days and a standard deviation of 7 days.

For what proportion of claims is the processing time expected to be longer than 8 days?

Give your answer to two decimal places in the form 0.xx.

Part B

The company is currently auditing the books of 40 small businesses. How many, to the nearest whole number are expected to take longer than 8 days to audit? Give your answer in the form xx or x as appropriate.

2)In this question, use Excel functions rather than Normal distribution tables.

The number of new cars sold by "Ma's New Car Factory" in a financial year can be approximated by a normal distribution with a mean of 125,000 cars and a standard deviation of 35,000 cars.

Part A

In order to recover all costs associated with the manufacture, they need to sell 100,000 cars. What is the probability that "Ma's New Car Factory" will do better than just covering their costs if the sales are distributed as expected? Give your answer to two decimal places in the form x.xx.

Part B

What is the number of cars sales that the company has only a 10% chance of achieving next year? Give your answer as a whole number.