During a calender year, the average electricity cost to run air-conditioning in an office is $830, with a standard deviation of $360. Assume the distribution of electricity costs for offices is unimodal and symmetric.

a) What is the probability of one office having an air conditioning electricity cost less than $800?

b) Now, if a random sample of 32 offices was selected, what is the probability that the average air conditioning electricity cost, for this sample, is less than $800?

c) Briefly explain the differences in your answers to part a) and part b).

d) Now, you are told that the population standard deviation is not known. What is the value of the population standard deviation, if the population mean is $830, the sample is size 32, and 69.5% of average electricity costs are less than $835?