00:01
For this problem, i first need to note that there is a little bit of missing data.
00:04
I was able to find this by looking up the question text, however.
00:07
So for everything here, we need to have a value for the population mean, mu, and a value for the standard deviation, which is 3 .1.
00:17
Though i'll say take the exact values with a grain of salt, especially if this is an online textbook, it's often done that the exact values will be randomized to some degree.
00:27
So emphasis here is on the procedure, not on the exact numbers.
00:32
That being said, we're being asked to convert x values or x intervals into z intervals.
00:38
So the idea is that z is equal to x minus mu over sigma.
00:44
Or for all of the values here, we'd find the corresponding z value given x by taking x minus 25 .5 divided by 3 .1.
00:54
So for part a, we have that x less than 30 becomes z less than, well, let's see here, that's going to be, 30 minus 25 .5 divided by 3 .1.
01:09
So that becomes z less than, rounded to two decimal places, 1 .45.
01:18
For part b, we have 19 is less than x.
01:24
The z score corresponding to 19 would be 19 minus 25 .5 divided by 3 .1...