00:01
This problem, we're given a normally distributed random variable x.
00:05
So x is normal, and we're told that the mean for this distribution is 83, and the standard deviation is 4.
00:16
And given this information, we want to compute a probability, namely that x is between 72 and 80.
00:25
So since x is normal, let me draw a normal curve for x.
00:30
Looks something like this.
00:31
The mean is in the middle, which is 83, and we're interested in the area under the curve between 72 and 80.
00:38
Both values lie to the left of the mean, so it's a strip of area under the curve that looks something like this.
00:46
So this probability here is equal to this area in red.
00:51
Now this is a normally distributed random variable, so i can go ahead and use the cumulative function for normal distributions to compute this probability...