CFA® Level 1: CFA® Level 1 Exam - Z-Score Calculation for Weekly Incomes

Calculating Z-Score for Weekly Incomes of Executives

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Question

The mean of a normally distributed group of weekly incomes of a large group of executive is $1,000 and the standard deviation is $100. What is the z-score for an income of $1,100?

Answers

Explanations

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A. B. C. D. E.

Explanation

z = (x-u)/sigma = 1100 - 1000/100 = 1.

To calculate the z-score for an income of $1,100, we need to use the formula for calculating the z-score:

z = (x - μ) / σ

Where:

  • z is the z-score
  • x is the value for which we want to find the z-score (in this case, $1,100)
  • μ is the mean of the distribution ($1,000)
  • σ is the standard deviation of the distribution ($100)

Substituting the given values into the formula, we have:

z = (1,100 - 1,000) / 100 z = 100 / 100 z = 1

Therefore, the z-score for an income of $1,100 is 1.

Looking at the provided answer options, we see that option E states the z-score as 1.00, which matches our calculated value. Hence, the correct answer is E.

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