Question

Use z scores to compare the given values. Who has the weight that is more extreme relative to the group from which they came: a male who weighs \( 1700 \mathrm{~g} \) or a female who weighs \( 1700 \m

Answer 1

Z-scores measure how far a value is from the mean in units of standard deviations. To calculate it, subtract the mean from the value and divide by the standard deviation. This allows comparison of values from different distributions.

Step-by-step explanation:

Understanding Z-Scores

To compare the weights of a male and a female relative to their groups, we use z-scores. A z-score indicates how many standard deviations an element is from the mean. The formula for calculating a z-score is:

Z = (X - μ) / σ

where X is the value, μ is the mean, and σ is the standard deviation.

For the example with weights for 80 cm girls, we calculate z-scores as follows:

1. For X = 11 kg (given μ = 10.2 kg and σ = 0.8 kg):
   
   Z = (11 - 10.2) / 0.8 = 1
2. For X = 7.9 kg (given μ = 10.2 kg and σ = 0.8 kg):
   
   Z = (7.9 - 10.2) / 0.8 = -2.875
3. For X = 12.2 kg (given μ = 10.2 kg and σ = 0.8 kg):
   
   Z = (12.2 - 10.2) / 0.8 = 2.5

A z-score of 1 indicates the weight is 1 standard deviation above the mean. A z-score of -2.875 indicates the weight is approximately 2.875 standard deviations below the mean. A z-score of 2.5 indicates the weight is 2.5 standard deviations above the mean.