Your message didn't come out clearly but I think the X followed by a box is meant to be X with a bar over it.

For 1 (a) The variance of sampling 3 bulbs isn't a third of the variance of sampling 1 bulb. You are confusing this with the variance of the sample mean which would be a third of the variance of 1 bulb if the central limit theorem applied to sample sizes as small as 3.

To go about this problem you should find the probability of 1 bulb being over 61 then cube that.

(b) here the total power is the sum of 3 normal distributions. The sum of normal distributions is itself a normal distribution with mean equal to the sum of the means and variance equal to the sum of the variances.

2. This is relating to confidence intervals. You know that a confidence interval is where If is to be within 0.2 of then E<0.2

In your answer I'm not sure where the 0.05 comes from.