Answer:
The z-score corresponding to an observed value of x of 2 is 0.215.
Step-by-step explanation:
We are given that a variable x has the possible observations shown below;
Possible observations of X: -3, -1, 0, 1, 1, 2, 4, 4, 5.
Firstly, we will find the mean and the standard deviation of X, i.e;
Mean of X, ([tex]\mu[/tex]) = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}[/tex]
= [tex]\frac{13}{9}[/tex] = 1.44
Standard deviation of X, ([tex]\sigma[/tex]) = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }[/tex]
= 2.603
Now, the z-score corresponding to an observed value of x of 2 is given by;
z-score = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{2-1.44}{2.603}[/tex] = 0.215.
