Question

Which of the following did you include in your response? Check all that apply.

a) The z-score for 2,500 g is –2.
b) According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.
c) 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.
d) Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.

Answer 1

To calculate the z-scores for the given weights, use the formula z = (x - μ) / σ. For each weight, calculate the z-score using the given mean and standard deviation. Interpret the z-scores as the number of standard deviations a weight is above or below the mean.

Step-by-step explanation:

To calculate the z-scores for the given weights, we need to use the formula: z = (x - μ) / σ where x is the given weight, μ is the mean, and σ is the standard deviation.

a) For a weight of 11 kg, the z-score is: z = (11 - 10.2) / 0.8 = 1. This means the weight is 1 standard deviation above the mean.

b) For a weight of 7.9 kg, the z-score is: z = (7.9 - 10.2) / 0.8 = -2.875. This means the weight is 2.875 standard deviations below the mean.

c) For a weight of 12.2 kg, the z-score is: z = (12.2 - 10.2) / 0.8 = 2.5. This means the weight is 2.5 standard deviations above the mean.