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Calculate the standard score of the given \( x \) value, \( x = 91.6 \), where \( \mu = 99.1 \), \( \sigma = 3.7 \). Round your answer to two decimal places.

Answer :

Final answer:

The standard score, or Z-score, is calculated using the formula Z = (X - μ) / σ. Substituting the given values into the formula, we get Z = -2.03, rounded to two decimal places.

Explanation:

To calculate the standard score, also known as the z-score, for the given value, we use the formula:

Z = (X - μ) / σ

Where:

  • X is the score you're interested in
  • μ is the mean score
  • σ is the standard deviation

In your question:

  • X = 91.6
  • μ = 99.1
  • σ = 3.7

Substituting these values into our formula, we get: Z = (91.6 - 99.1) / 3.7

We calculate 91.6 - 99.1 to get -7.5, and then divide this number by 3.7 to get the z-score, or the standard score.

The final answer, rounded to two decimal places, is -2.03.

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