Finding z-scores

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of a distribution.

Front

How do you calculate a z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean.

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean.

Front

If a student scores 31 on the ACT with a mean of 21 and a standard deviation of 5, what is the z-score?

Back

Z-score = (31 - 21) / 5 = 2.00.

Front

If a home costs $193,000 with a mean of $200,000 and a standard deviation of $10,000, what is the z-score?

Back

Z-score = (193,000 - 200,000) / 10,000 = -0.70.

Front

What weight corresponds to a z-score of -2 for wallabies with a mean of 9lbs and a standard deviation of 1.5lbs?

Back

Weight = μ + (z * σ) = 9 + (-2 * 1.5) = 6lbs.

Front

What is the z-score for a student who scores 28 on the ACT with a mean of 21 and a standard deviation of 5?

Back

Z-score = (28 - 21) / 5 = 1.40.

Front

If a student has a z-score of 2.34 in chemistry, what does it imply about her performance?

Back

It implies she performed significantly better than her peers in chemistry.

Front

If a student has a z-score of 1.52 in English, how does it compare to her chemistry score?

Back

She performed better in chemistry since 2.34 > 1.52.