00:01
So in this question, we're going to examine the results of the 2014 -2015 sat math exam with a mean of 501 and a standard deviation of 117 as reported in a table that you be given.
00:15
In part a, we want to know what percentage of seniors scored lower than 300 on the math sat.
00:23
And so what we're going to have to do is convert 300 from a raw score into a z score.
00:31
What do i know about computing z scores? well, i know that z is equal to x minus mu over sigma, where mu is my mean, sigma is my standard deviation.
00:47
So my x is 300, my mean is 501, and my standard deviation is 117.
00:56
So i'm going to head to my calculator, 300 minus 501.
01:01
I divide that by 117, and i am getting a z score this time of about negative 1 .72, rounding to two decimal places, negative 1 .72.
01:14
If i head to my z score table, i see that negative 1 .72 corresponds to 0 .04272.
01:26
That's the area to the left of that z score, converting into a percent.
01:30
I'm going to say that approximately 4 .27 % of the seniors scored lower than 300 on the math sat.
01:44
In part b, we say what percentage scored between 600 and 700 points.
01:51
So i'm going to have to figure out the z scores for both 600 and 700.
01:56
Again, i'm using x minus mu over sigma.
02:00
So for a score of 600, i have a z score of 600, minus 501 over 117.
02:11
That's 99.
02:13
Over 117, i'm getting a z score of about 0 .85.
02:21
Now, what does a c score of 0 .085 correspond to? corresponds to about 0 .802 or 80 .2%.
02:33
And so i'm saying that 80 .2 % scored below 600.
02:41
Now i need to get my z score associated with 700...