Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams while babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 395 grams. If a 35​-week gestation period baby weighs 2850 grams and a 41​-week gestation period baby weighs 3150 ​grams, find the corresponding​ z-scores. Which baby weighs more relative to the gestation​ period? Find the corresponding​ z-scores. Which baby weighs relatively more​? Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

The 35-week gestation period baby has a z-score of 0.7.

The 41-week gestation period baby has a z-score of 0.89

Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Which baby weighs more relative to the gestation​ period?

The baby with the higher z-score.

35​-week gestation period baby weighs 2850 grams

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams

This means that Z is found when $X = 2850, \mu = 2500, \sigma = 500$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2850 - 2500}{500}$

$Z = 0.7$

The 35-week gestation period baby has a z-score of 0.7.

41​-week gestation period baby weighs 3150 ​grams.

Babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 395 grams.

This means that Z is found when $X = 3150, X = 2800, \mu = 395$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3150 - 2800}{395}$

$Z = 0.89$

The 41-week gestation period baby has a z-score of 0.89

Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.