00:01
The ph measurements of water specimens from various locations along a given river basin are normally distributed with a mean of 8 and a standard deviation of 0 .3.
00:13
What is the approximate probability that the ph measurement of a randomly selected water specimen is a value between 7 .5 and 8 .2? so the probability that x is between 7 .5 and 8 .2 in a normal distribution, can be found by finding the probability of 7 .5 minus that mu of 8 divided by our standard deviation.
00:43
And then we'll do the same thing for the upper value as well.
00:48
So 8 .2 minus mu divided by sigma.
00:52
And what that does is that gives us z values from our standard normal table.
00:57
So we have negative 1 .67 is less than z, which is less than positive .67.
01:02
And now we can look up those proportions or probabilities in this.
01:05
Case in the table.
01:08
So 0 .67 has a probability of 0 .7486, negative 1 .67 has a probability of 0 .0475, and the probability in between them can be found by subtracting, and that would be 0 .7011.
01:24
For part b, what is the 40th percentile? so the 40th percentile, the first thing we need to do is we need to find a z score or a z value that corresponds to that proportion of 0 .4.
01:38
For me, i chose negative 0 .25 looking at my table.
01:43
So i'm going to find my mean by taking my mu plus my standard deviation times that z value i just looked up.
01:53
And when i calculate that, i get 7 .925...