Question

Here are summary statistics for randomly selected weights of newborn girls: n = 36, x=3180.6 g, s = 700.5 g.

a. Identify the critical value to/2 used for finding the margin of error. tₓ/₂ = = 2.02 (Round to two decimal places as needed.)

Answer 1

The z-scores for weights of 11 kg, 7.9 kg, and 12.2 kg are calculated using the formula Z = (X - μ) / σ, resulting in z-scores of 1, -2.875, and 2.5 respectively. These scores indicate how many standard deviations each weight is from the mean, with positive values being above the mean and negative ones below.

Step-by-step explanation:

When calculating the z-scores for the given weights of newborn girls, the formula to use is:

Z = (X - μ) / σ,

where X is the weight of the child, μ is the mean weight, and σ is the standard deviation. Applying this formula to the given weights:

1. For 11 kg: Z = (11 - 10.2) / 0.8 = 1,
2. For 7.9 kg: Z = (7.9 - 10.2) / 0.8 = -2.875,
3. For 12.2 kg: Z = (12.2 - 10.2) / 0.8 = 2.5.

The z-score tells us how many standard deviations a data point is from the mean. A positive z-score indicates the weight is above the mean, while a negative z-score suggests it is below the mean. The Z-scores obtained indicate:

• 11 kg is 1 standard deviation above the mean,
• 7.9 kg is approximately 2.875 standard deviations below the mean,
• 12.2 kg is 2.5 standard deviations above the mean.