00:01
Hello student, the development psychologist was interested in how long it will take a particular 7 year old child to complete the three different aptitude tests as compared with the 7 year old in the general population.
00:13
So the given information is for the first population, they give the child time for the reading was 31 minutes.
00:28
So x is equal to 31 and the mean is equal to 29 and the standard deviation is equal to 4 for the first population.
00:38
And for the math, that is, we can see the second population 26 minutes, that is x equals to 26, mean is equal to 32 and the standard deviation equals to 2.
00:51
For science, the value of x, that is 40 minutes, the mean is equal to 31 and the standard deviation is equal to 4.
01:03
And the first question is that calculate the child's z score for each of the aptitude tests.
01:09
So we know that the z score is equal to x minus m divided by standard deviation.
01:18
For the first, that is the first population, the z1 is equal to, it will be x1 m1 sd1, x2 m2 sd2, x3 m3 sd3.
01:33
So z1 is equal to x1 minus m1 divided by sd1, put the values here, 31 minus 29 divided by 4.
01:42
And after simplification, we get this value as 31 minus 29 divided by 4 equals to 0 .5.
01:54
So for the first population, we get z1 is equal to 0 .5.
02:00
Now for the second, that is the math, z2 is equal to x2 minus m2 divided by standard deviation 2.
02:10
The value of x2 is 26 minus 32 divided by 2.
02:14
After simplification, we get the value as minus 3.
02:18
Therefore, z2 is equal to minus 3...