Question

Babies born after a gestation period of 32-35 weeks have a mean weight of 2700 grams and a standard deviation of 700 grams, while babies born after 40 weeks have a mean weight of 3000 grams and a standard deviation of 490 grams. If a 33-week gestation baby weighs 2950 grams and a 40-week gestation baby weighs 3150 grams, which baby weighs more relative to other babies of the same gestation period? The 33 week or the 40 week baby?

Answer 1

Explanation:

4000 grams

Answer 2

The 33 week gestation period baby has the higher z-score, so he weighs more relative to other babies of the same gestation period.

Explanation:

Problems of normally distributed samples can be 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 = (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.

Who weighs more relative to other babies of the same gestation period?

Whoever has the higer z-score

33 - week baby.

Babies born after a gestation period of 32-35 weeks have a mean weight of 2700 grams and a standard deviation of 700 grams. A 33-week gestation baby weighs 2950 grams.

We have to find z when
`\mu = 2700, \sigma = 700, X = 2950`. So

`Z = (X - \mu)/(\sigma)`

`Z = (2950 - 2700)/(700)`

`Z = 0.357`

40-week baby

Mean weight of 3000 grams and a standard deviation of 490 grams. 40-week gestation baby weighs 3150 grams.

We have to find Z when
`\mu = 3000, \sigma = 490, X = 3150`. So

`Z = (X - \mu)/(\sigma)`

`Z = (3150 - 300)/(490)`

`Z = 0.306`

The 33 week gestation period baby has the higher z-score, so he weighs more relative to other babies of the same gestation period.