Questions: Calculate the standard score of the given X value, X=75.1, where μ=68.3 and σ=71.8. Round your answer to two decimal places.

Calculate the standard score of the given X value, X=75.1, where μ=68.3 and σ=71.8. Round your answer to two decimal places.
Transcript text: Calculate the standard score of the given $X$ value, $X=75.1$, where $\mu=68.3$ and $\sigma=71.8$. Round your answer to two decimal places.
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Solution

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Solution Steps

Step 1: Given Values

We are given the following values:

  • X=75.1 X = 75.1
  • μ=68.3 \mu = 68.3
  • σ=71.8 \sigma = 71.8
Step 2: Calculate the Z-score

The Z-score is calculated using the formula:

z=X−μσ z = \frac{X - \mu}{\sigma}

Substituting the given values:

z=75.1−68.371.8 z = \frac{75.1 - 68.3}{71.8}

Calculating the numerator:

75.1−68.3=6.8 75.1 - 68.3 = 6.8

Now substituting back into the Z-score formula:

z=6.871.8≈0.0947 z = \frac{6.8}{71.8} \approx 0.0947

Rounding to two decimal places, we find:

z≈0.09 z \approx 0.09

Final Answer

The Z-score is \\(\boxed{0.09}\\).

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