The nails are produced with a mean length of 6 cm (centimetres). Because of the manufacturing process imperfections, the lots of nails are approximately normally distributed with a standard deviation of 0.03 cm.

1. What proportion of nails is made longer than 6 cm?

2. What proportion of nails is made longer than 6.03 cm?

3. Any nails shorter than 5.95 cm or longer than 6.05 cm are rejected. What proportion of the nails will be rejected?

4. If 40,000 nails were to be produced, how many would the manager have to reject?

5. If there is an order for 60,000 nails and it states the nails must be between 5.96 cm and 6.04 cm long, how many

should the manager order to produce?