Question

A doctor has found that, over the years, 95% of the babies he has delivered weighed x pounds, where 8.4a) 8.4b) 7.2c) 6.0d) 5.0

Answer 1

Z-scores are calculated using the formula z = (X - μ) / σ, where X is the weight of the child, μ is the mean, and σ is the standard deviation. For the weights 11 kg, 7.9 kg, and 12.2 kg, the corresponding z-scores are 1, -2.875, and 2.5, indicating their positions relative to the mean weight of the reference population.

Step-by-step explanation:

The student has asked for the calculation and interpretation of z-scores that correspond to given weights. In statistics, a z-score measures the number of standard deviations an element is from the mean. To calculate the z-scores for the provided weights of All 80 cm girls from a reference population with mean μ = 10.2 kg and standard deviation σ = 0.8 kg, we use the formula z = (X - μ) / σ. The z-scores for the given weights are as follows:

• 11 kg: z = (11 - 10.2) / 0.8 = 1. This means the weight of 11 kg is 1 standard deviation above the mean.
• 7.9 kg: z = (7.9 - 10.2) / 0.8 = -2.875. This weight is 2.875 standard deviations below the mean.
• 12.2 kg: z = (12.2 - 10.2) / 0.8 = 2.5. This weight is 2.5 standard deviations above the mean.

The z-scores help understand how each weight compares with the average weight (mean) of the reference population. Positive z-scores indicate weights above the mean, while negative z-scores indicate weights below the mean.