ASRJC Normal Distribution Tutorial 23 Q6

The daily consumption of electricity per house is an estate with \(200\) similar houses has a normal distribution with mean \(80\) units and standard deviation \(20\) units. The daily consumption of electricity in each house is independent of the consumption of the other houses.

1. Find the probability that on a given day, a house selected at random consumes not less than \(40\) units and not more than \(110\) units.
2. Find the probability that on a given day, a house selected at random consumes not less than \(40\) units given that it consumes not more than \(110\) units.
3. Find the probability that, on a given day, not more than \(20\) houses have consumption in excess of \(110\) units.
4. If the daily consumption of electricity for the whole estate exceeds a certain value \(A\) on only \(5\%\) of all recorded days, find this value of \(A\) to the nearest integer.