(i) A random sample of 64 households in a town was selected and the mean electricity usage was found to be 425 KWH and standard deviation of 72 KHW. Calculate the 99% confidence interval for the mean electricity usage of households in that town. (3 marks)

(ii) Compute the 98% confidence interval if in another town, a sample of 14 households revealed that the mean of electricity usage, which is assumed to be normally distributed, was 518 KWH and standard deviation of 54KWH.

(i) In a bakery, out of a sample of 180 breads, it was found that 45 of them were below prescribed standards. Calculate a 99% confidence interval for the proportion of bread being below the prescribed standards. (4 marks)

(ii) In another sample of 400 breads, it was found that 128 of them were below the prescribed standards. Explain at 95% confidence limit, what size sample would have to be taken in order to estimate the percentage 2%. (6 marks)

(iii) The breads are packed into bags before being delivered to selling points. Calculate a 90% confidence interval for the mean bag if in a sample of 60 bags of breads, the mass, x kgs, gave x= 420 kgs and x2 = 4190 kgs