Question

Solve the problem. A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 2.

Answer 1

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, ($\mu$) = $\frac{\sum X}{n}$

                       =  $\frac{(-3)+ (-1)+ 0+ 1+ 1+ 2+ 4+ 4+ 5}{9}$  

                       =  $\frac{13}{9}$  = 1.44

Standard deviation of X, ($\sigma$) =  $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$

                            =  $\sqrt{\frac{(-3-1.44)^{2}+(-1-1.44)^{2}+......+(4-1.44)^{2}+(5-1.44)^{2} }{9-1} }$

                            =  2.603

Now, the z-score corresponding to an observed value of x of 2 is given by;

                  z-score =  $\frac{X-\mu}{\sigma}$

                               =  $\frac{2-1.44}{2.603}$  = 0.215.