00:01
The monthly consumption of electrical power is normally distributed with a mean of 60 ,000 kilowatt hours and a standard deviation of 400 kilowatt hours.
00:13
For part a, we were asked, what is the probability that the monthly consumption will be less than 59 ,100? so we want the probability that x is smaller than 59 ,100.
00:29
So visually, if this graph represents the monthly power consumption, we have the mean mean of 60 ,000 in the center.
00:39
59 ,100 is somewhere around here.
00:43
Probability that the consumption is less than that is equal to the area under the curve and to the left of it.
00:52
One way to solve this probability is to use a standard normal table, in which case we first have to standardize the random variable according to this formula.
01:03
If we do so, this is equal to the probability that z is less than minus 2 and a quarter.
01:13
Let's look up z equals minus 2 and a quarter in the standard normal table.
01:18
That corresponds to a cumulative probability of 0 .0122.
01:34
And for question b we want the probability that the consumption is between 59 ,000 and 60 ,300.
01:52
So the first step is to first express these in terms of cumulative probabilities.
01:58
This is equal to the probability that x is less than 69 ,300 minus the probability that that x is at most 59 ,000...