Questions: When Steve Jobs was Chief Executive Officer (CEO) of Apple, he earned an annual salary of 1. The CEOs of the 50 largest U.S. companies had a mean salary of 1,449,779 and a standard deviation of 527,651 (based on data from USA Today)
Convert Steve Jobs' salary to a z score. Round to 2 decimals.
z =
Transcript text: Question 19
1 pts
When Steve Jobs was Chief Executive Officer (CEO) of Apple, he earned an annual salary of \$1. The CEOs of the 50 largest U. S. companies had a mean salary of $\$ 1,449,779$ and a standard deviation of $\$ 527,651$ (based on data from USA Today)
Convert Steve Jobs' salary to a z score. Round to 2 decimals.
\[
z=\square
\]
Solution
Solution Steps
To convert Steve Jobs' salary to a z score, we use the formula for the z score:
\[ z = \frac{X - \mu}{\sigma} \]
where \( X \) is Steve Jobs' salary, \( \mu \) is the mean salary, and \( \sigma \) is the standard deviation. Plug in the given values and calculate the z score.
Step 1: Identify the Given Values
We are given:
Steve Jobs' salary \( X = 1 \)
Mean salary \( \mu = 1,449,779 \)
Standard deviation \( \sigma = 527,651 \)
Step 2: Apply the Z Score Formula
The formula for the z score is:
\[ z = \frac{X - \mu}{\sigma} \]
Step 3: Substitute the Given Values
Substitute the given values into the formula:
\[ z = \frac{1 - 1,449,779}{527,651} \]
Step 4: Calculate the Z Score
Perform the calculation:
\[ z = \frac{-1,449,778}{527,651} \approx -2.7476 \]
Step 5: Round the Z Score
Round the z score to 2 decimal places:
\[ z \approx -2.75 \]