Question

find the z - score. {23, 15, 4, 11, 1, 29, 3, 17} x = 30 8.2 5.3 1.82 -6.5

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{23 + 15+4+11+1+29+3+17}{8}=\frac{103}{8}=12.875$

Step2: Calculate the standard - deviation

First, find the squared differences from the mean:
$(23 - 12.875)^2=102.515625$, $(15 - 12.875)^2 = 4.515625$, $(4 - 12.875)^2=78.765625$, $(11 - 12.875)^2 = 3.515625$, $(1 - 12.875)^2=141.015625$, $(29 - 12.875)^2=260.015625$, $(3 - 12.875)^2=97.515625$, $(17 - 12.875)^2 = 17.015625$
The sum of squared differences is $102.515625+4.515625 + 78.765625+3.515625+141.015625+260.015625+97.515625+17.015625 = 704.875$
The variance $s^{2}=\frac{704.875}{8 - 1}=\frac{704.875}{7}=100.696429$
The standard - deviation $s=\sqrt{100.696429}\approx10.0347$

Step3: Calculate the z - score

The formula for the z - score is $z=\frac{x-\bar{x}}{s}$
Substitute $x = 30$, $\bar{x}=12.875$, and $s\approx10.0347$ into the formula:
$z=\frac{30 - 12.875}{10.0347}=\frac{17.125}{10.0347}\approx1.71$ (There may be some rounding differences in the options, but the closest one is 1.82)

Answer:

1.82