00:01
In this question, we have the given data is as follows.
00:07
So we have the values 13 9 16 18 14 10 12 11 and 11.
00:20
So first let's find the mean of the given data.
00:24
So we know that mean is calculated as sum of the given values divided by the number of values.
00:33
So here on adding all the values 13 plus 19 plus 16 plus 18 and so on till 11 we get 114 divided by there are total 9 values.
00:44
Therefore n value is equal to 9.
00:46
So from this we get mean value is equal to 12 .7 and standard deviation standard deviation, which is calculated using the formula square root of summation xi minus x bar whole square divided by n minus 1.
01:09
So on calculating this we get the required value of standard deviation sigma is equal to 2 .75.
01:18
Now, we know that the z score is calculated as z score is equal to x minus mean mu divided by standard deviation sigma.
01:30
So for we have z is equal to 0 we can find the x value will be equal to z sigma plus mu.
01:42
So on plugging in the values we have x is equal to z is 0 times of sigma will be 0 plus mean mu is 12 .7.
01:53
So for z is equal to 0 we have x is equal to 12 .7.
01:58
So this is one match that we have found now next for z is equal to 1 .25...