An energy company provides services for a town of n=10,000 households. For a household, the size of monthly energy consumption is exponentially distributed with a mean of 800 kwh, and does not depend on the consumption of other households. The company has specified a consumption baseline d which is not exceeded by 70% of households on the average. (That is, the expected proportion of the households with consumption less than d, is 0.7.) The company charges 12¢ per one kwh the households with consumption less than d, and charges 15¢/kwh for a surplus over d. 

(a) Let M be the proportion of households with a consumption less than d, and let k be a number such that M > k with probability 0.9. Do you expect k to be less or larger than 0.7? Estimate k using normal approximation.

(b) The total payment of all households with probability 0.9 is larger than what amount?