00:01
For this problem, a broadcasting executive is telling us that they believe ratings of shows are normally distributed.
00:10
So let's let x be the rating of a randomly selected show.
00:14
This is a normal random variable.
00:16
And he suspects that the mean is 18 .2 and the standard deviation is 1 .6.
00:23
And given this information, we want to figure out what the, uh, what rating will be such that the area to the left of that rating under the curve for this normal distribution will be 0 .2.
00:37
Let me just draw that.
00:40
So if we've got a normal distribution here for x, the mean is going to be in the middle, 18 .2, and the curve will be symmetric about the mean.
00:49
And we want to find the rating, let's call it, uh, p20 for 20th percentile, uh, such that the area to the left of this rating is equal to 0 .2.
01:02
So this area in red here to the left of p20 is 0 .2, and we want to find this.
01:10
So we can start by writing down a cumulative probability for x, namely the probability that x is less than p20 is equal to 0 .2, just by definition.
01:23
And now how do we find p20? well, since x is normally distributed, we can use the inverse normal function on some piece of technology in order to get this, uh, value out...