00:01
In this problem variable x follows the normal distribution and population mean mu is 134.
00:14
Population standard deviation sigma is 59 .9.
00:21
And sample size n is 184.
00:26
The task is to find p35.
00:30
The score that separates the bottom 35 % scores from the top 65 % scores.
00:41
So we should find for single values and for sample means.
00:48
Firstly, let's find for single values.
00:51
We can write that probability x is less than unknown value x equal to 0 .3 or 35%.
01:06
Next probability that z is less than unknown value z equals to 0 .35.
01:16
And now by using z score table, we can find the corresponding value of the z score minus 0 .385.
01:30
So now let's remind the formula for the z score for single value.
01:35
X minus mu divided by sigma let's use data minus 0 .385 equals to x minus 134 divided by 59 .9...