00:01
In this exercise, we are told that the distance traveled per truck per year, let's call that random variable x, is normally distributed with a mean of 70 ,000 miles and a standard deviation of 11 ,000 miles.
00:17
And the question we want to answer is how many miles will be traveled by at least 75 % of the trucks.
00:24
So if this graph represents the normal distribution of the distances traveled by the trucks in a year has a mean of 70 ,000 miles, standard deviation of 11 ,000.
00:36
And so there exists some distance such that 67 % of the distribution is at least that far, travels at least that far.
00:49
So in other words, the area under the curve and to the right of this distance has an area of 0 .75.
01:04
So it means that 75 % of the trucks travel at this distance or greater.
01:12
So mathematically we can write it like this.
01:14
The probability of x being at least this distance is 0 .75...