6 The lifetimes, in hours, of a particular type of light bulb are normally distributed with mean 2000 hours and standard deviation \(\sigma\) hours. The probability that a randomly chosen light bulb of this type has a lifetime of more than 1800 hours is 0.96 .

1. Find the value of \(\sigma\).
   New technology has resulted in a new type of light bulb. It is found that on average one in five of these new light bulbs has a lifetime of more than 2500 hours.
2. For a random selection of 300 of these new light bulbs, use a suitable approximate distribution to find the probability that fewer than 70 have a lifetime of more than 2500 hours.
3. Justify the use of your approximate distribution in part (ii).