5 Plastic drinking straws are manufactured to fit into drinks cartons which have a hole in the top. A straw fits into the hole if the diameter of the straw is less than 3 mm . The diameters of the straws have a normal distribution with mean 2.6 mm and standard deviation 0.25 mm .

1. A straw is chosen at random. Find the probability that it fits into the hole in a drinks carton.
2. 500 straws are chosen at random. Use a suitable approximation to find the probability that at least 480 straws fit into the holes in drinks cartons.
3. Justify the use of your approximation.