00:01
All right, in your question, you're told that the speeds of drivers on a section of road is normally distributed with a mean of 32 and a standard deviation of 6 .2.
00:16
And you have three parts of this question.
00:18
The first part is to find the probability that a randomly selected driver would be driving less than 31 miles per hour.
00:27
Okay, so i drew a sketch of the normal model because we were told, normal distribution that places the mean 32 at the center and 31 would just be to the left of that and we want the probability of the speed being lower than that number which would be to the left so to do this i'm going to use a program called normal cdf and this is typically found on most graphing calculators or computer programs that are working with statistics i'm using a t i 84 and it's found under the second, hit the second key, then the distribution key.
01:14
And the way this will work is the first number i type in is the lower boundary of the region we're working with.
01:23
So we want to be less than this 31.
01:25
So basically we're heading to negative infinity.
01:29
So i'm going to put in negative 1 million.
01:35
And basically, if you're at the left tail for a boundary, put in negative 1 million.
01:39
And then the program, if you're at the right tail, put in one million.
01:43
You just need a very large or very small number.
01:46
But the first number in the program is always the lower boundary.
01:51
Then the upper boundary is 31, and then we place in our mean 32, and our standard deviation of 6 .2.
02:04
We take that into the calculator here and we'll have a result.
02:19
Okay, that works out to be to three decimal places.
02:23
0 .436.
02:28
Now in part b, you want to look for the probability that someone is speeding, so that's over 35 miles an hour.
02:36
I don't, if you were equal to it, it wouldn't be speeding.
02:39
So i took away my equal bar.
02:40
It really doesn't matter, though, in our calculation.
02:44
The normal model for this probability is drawn here, and we want to find the area or the probability on the right side of 35...