Answer:
[tex]\boxed {\boxed {\sf z= -0.1}}[/tex]
Step-by-step explanation:
A z-score helps describe the relationship between a value and the mean of a group of values. Basically, it tells us how many standard deviations away from the mean a value is. The formula is:
[tex]z= \frac{x- \mu}{\sigma}[/tex]
where x is the value, μ is the mean, and σ is the standard deviation.
For this standardized exam, the mean is 350 and the standard deviation is 40. We want to find the z-score for a value of 346.
Substitute the values into the formula.
[tex]z= \frac{ 346-350}{40}[/tex]
Solve the numerator.
[tex]z- \frac{ -4}{40}[/tex]
Divide.
[tex]z= -0.1[/tex]
The z score is -0.1, so the person with a score of 346 on the exam was 0.1 standard deviations lower than the mean.
