00:01
Firstly, let's summarize this problem.
00:04
We have a set of data that is normally distributed with population mean mu equals 200, and population standard deviation sigma equals 47.
00:26
And this problem has two parts.
00:29
Part a, we should determine the value.
00:34
Of x from the following information 60 % of the values are greater than x so this can be written as probability that x is greater than some unknown value x equals 0 .60 or 60 % this can be written as p x is less than unknown value x equals 1 minus 0 .60 and this equals 0 .4.
01:20
The next stage we can write that p z is less than some unknown value z will be 0 .4.
01:34
And by using z score table, we can find the corresponding value of that score and can write that p that is less than minus 0 .253 equals 0 .4.
01:59
Let's remind the formula for the z score.
02:08
Sigma let's use data minus 0 .253 equals x minus population mean 200 divided by standard deviation 47.
02:27
Let's solve for x x will be 200 minus 0 .253 times 47.
02:47
And the final value will be x equals 188 .1.
02:56
So this is the answer for the part a.
03:00
The next one, part b.
03:08
X is less than 16 % of the values.
03:14
This can be written as probability that x is less than unknown value x equals 0 .17.
03:26
We can write that p z is less than unknown value z equals 0 .17.
03:38
And by using that score table we can find the corresponding value of z and can write that p z is less than minus minus 0 .954 equals 0 .17.
04:04
Let's use that score formula and we can write minus 0 .954 equals x minus population mean 200 divided by standard deviation 47.
04:25
Let's solve for x.
04:31
X will be 200 minus 0 .954 times 47.
04:44
And this equals 155 .0 .16...