00:01
This problem we have a sample and the task is to find the z score for all five observations.
00:10
Firstly, let's remind the formula for the z score that equals x minus sample mean x bar divided by sample standard deviation s.
00:23
So firstly, let's calculate sample mean and sample standard deviation.
00:27
We see that the sample size n equals 5 because we have five different values and now let's calculate sample mean x bar it equals some of each value divided by sample size.
00:46
So in this case x bar equals 62 plus 90 plus 50 plus 50 plus 86 plus 72 divided by 5 and we obtain sample mean equals 72.
01:12
Now let's remind the formula for the sample standard deviation as it equals root square of the sum of difference xe minus x bar square divided by n minus 1.
01:33
So let's calculate s equals root square, 62 minus 72 square plus 90 minus 72 square plus 50 minus 72 square plus 80 minus 72 square plus 806 minus 72 square plus 72 square and this will be divided by 5 minus 1.
02:26
So the whole root square and the next stage of calculation as equals root square of 100 plus 340 24 plus 484 plus 196 plus 0 divided by 4 and s equals root square of 276 and this equals 16 .61.
03:19
Now we are ready to find the needed z scores...