Answer:
The sample mean is 3 and the sample standard deviation is 2.
Step-by-step explanation:
The formula to compute the sample mean ([tex]\bar x[/tex]) and sample standard deviation (s) is:
[tex]\bar x=\frac{1}{n}\sum x\\s=\frac{1}{n-1}\sum (x-\bar x)^{2}[/tex]
The sample is, S = {5, 0, 4, 5, 1, 2, 4}.
The sample is of size n = 7.
Compute the sample mean value as follows:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{7}(5+0+4+5+1+2+4)=3[/tex]
The sample mean is 3.
Compute the sample standard deviation is:
[tex]s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}} \\=\sqrt{\frac{1}{7-1}[(5-3)^{2}+(0-3)^{2}+(4-3)^{2}+...+(4-3)^{2}]}\\=\sqrt{\frac{1}{6}\times 24}\\=\sqrt{4}\\=2[/tex]
The sample standard deviation is 2.
The formula to compute the z-score of a sample values x is:
[tex]z=\frac{x-\bar x}{s}[/tex]
Compute the z-scores for all the sample values as follows:
[tex]z=\frac{x-\bar x}{s}=\frac{5-3}{2}=1[/tex]
[tex]z=\frac{x-\bar x}{s}=\frac{0-3}{2}=-1.5[/tex]
The remaining values are computed similarly in the table.
Now it is provided that the population mean and standard deviation are:
M = 50
S = 10
Transform each z-scores computed, into new sample values using the formula:
[tex]z=\frac{X-M}{S}\\z=\frac{X-50}{10}\\X=10z+50[/tex]
The new sample values are computed in the table below.
