Questions: Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 460 grams. If a 34-week gestation period baby weighs 2400 grams and a 40-week gestation period baby weighs 2700 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period? The 34-week gestation period baby weighs standard deviations the mean. The 40-week gestation period baby weighs standard deviations the mean. (Round to two decimal places as needed.)

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 460 grams. If a 34-week gestation period baby weighs 2400 grams and a 40-week gestation period baby weighs 2700 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period?

The 34-week gestation period baby weighs  standard deviations  the mean.
The 40-week gestation period baby weighs  standard deviations  the mean.
(Round to two decimal places as needed.)
Transcript text: Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2900 grams and a standard deviation of 800 grams while babies born after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 460 grams. If a 34 -week gestation period baby weighs 2400 grams and a 40 -week gestation period baby weighs 2700 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period? The 34 -week gestation period baby weighs $\square$ standard deviations $\square$ the mean. The 40 -week gestation period baby weighs $\square$ standard deviations $\square$ the mean. (Round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Z-score for the 34-week gestation period baby

The formula for calculating the z-score is:

\[ z = \frac{X - \mu}{\sigma} \]

where \(X\) is the observed value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

For the 34-week gestation period baby:

  • \(X = 2400\) grams
  • \(\mu = 2900\) grams
  • \(\sigma = 800\) grams

Substitute these values into the formula:

\[ z = \frac{2400 - 2900}{800} = \frac{-500}{800} = -0.625 \]

Step 2: Calculate the Z-score for the 40-week gestation period baby

For the 40-week gestation period baby:

  • \(X = 2700\) grams
  • \(\mu = 3200\) grams
  • \(\sigma = 460\) grams

Substitute these values into the formula:

\[ z = \frac{2700 - 3200}{460} = \frac{-500}{460} \approx -1.0869 \]

Step 3: Compare the Z-scores

The z-score indicates how many standard deviations an observation is from the mean. A more negative z-score indicates that the observation is further below the mean.

  • The 34-week gestation period baby has a z-score of \(-0.625\).
  • The 40-week gestation period baby has a z-score of \(-1.0869\).

Since \(-1.0869\) is more negative than \(-0.625\), the 40-week gestation period baby weighs less relative to its gestation period.

Final Answer

The 34-week gestation period baby weighs \(\boxed{-0.63}\) standard deviations below the mean.
The 40-week gestation period baby weighs \(\boxed{-1.09}\) standard deviations below the mean.
The 40-week gestation period baby weighs less relative to the gestation period.

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