(ii) The probability that a light bulb has a lifetime of more than 2500 hours is 0.2. For 300 bulbs, the mean is calculated as:

\(\text{Mean} = 300 \times 0.2 = 60\)

The variance is:

\(\text{Variance} = 300 \times 0.2 \times 0.8 = 48\)

We use the normal approximation to the binomial distribution. The probability that fewer than 70 bulbs have a lifetime of more than 2500 hours is:

\(P(X < 70) = P\left(Z > \frac{69.5 - 60}{\sqrt{48}}\right)\)

\(= \Phi(1.371)\)

\(= 0.915\)

(iii) The conditions for using the normal approximation are met because:

\(np = 60\) and \(nq = 240\), both greater than 5.