Calculate the standard score ( $$ z $$-score) of the given sample mean. Round your answer to two decimal places. $$ \mu=57 \text { and } \sigma=14 ; n=38 ; \bar{x}=62 $$

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To calculate the standard score (z-score) of the given sample mean, we can use the formula:

$$ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $$

Given:
- Population mean ($$ \mu $$) = 57
- Population standard deviation ($$ \sigma $$) = 14
- Sample size ($$ n $$) = 38
- Sample mean ($$ \bar{x} $$) = 62

Substitute the values into the formula and calculate the z-score.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(62-57\right)}{\left(\frac{14}{\sqrt{38}}\right)}$$
- step1: Remove the parentheses:
  $$\frac{62-57}{\frac{14}{\sqrt{38}}}$$
- step2: Subtract the numbers:
  $$\frac{5}{\frac{14}{\sqrt{38}}}$$
- step3: Multiply by the reciprocal:
  $$5\times \frac{\sqrt{38}}{14}$$
- step4: Multiply:
  $$\frac{5\sqrt{38}}{14}$$
The standard score (z-score) of the given sample mean is approximately 2.20 when rounded to two decimal places.
The z-score of the sample mean is approximately 2.20.

Calculate the standard score ( -score) of the given sample mean. Round your answer to two decimal places.

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