State four properties of the normal distribution.

(b) (i)The temperature in a city is a random variable having a normal distribution with mean 24C and standard deviation of 3C. What is the probability that on a particular day, the temperature is

(1) More than 28C

(2) Less than 22C

(ii) In another city, the maximum temperature in the month of April is normally distributed with a mean of 23C and standard deviation 4C. Calculate the number of days in April which is to be expected to reach a maximum of 22C to 27C.

(c) (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.

(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.

(d) (i) In a bakery, out of a sample of 180 breads, it was found that 45 of them were below prescribed standards. Calculate a 95% confidence interval for the proportion of bread being below the prescribed standards.

(ii) 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.