Question

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3400 grams and a standard deviation of 425 grams. If a 34-week gestation period baby weighs 2700 grams and a 40-week gestation period baby weighs 3300 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 deviation the mean. (Round to two decimal places as needed.) Which baby weighs relatively less? A. The baby born in week 40 does since its z-score is smaller. B. The baby born in week 34 does since its z-score is larger. C. The baby born in week 34 does since its z-score is smaller. D. The baby born in week 40 does since its z-score is larger.

Answer 1

Answer:

The 34 week gestation's period baby weighs 0.11 standard deviations below the mean.

The 41 week gestation's period baby weighs 0.24 standard deviations below the mean.

A. The baby born in week 40 does since its z-score is smaller.

Step-by-step explanation:

Normal model problems can be solved by the zscore formula.

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$, the z-score of a value X is given by:

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

The zscore represents how many standard deviations the value of X is above or below the mean[/tex]\mu[/tex]. Whoever has the lower z-score weighs relatively less.

Find the corresponding z-scores.

Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 900 grams. A 34-week gestation period baby weighs 2700 grams.

Here, we have $\mu = 2800, \sigma = 900, X = 2700$.

So

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

$Z = \frac{2700 - 2800}{900}$

$Z = -0.11$

A negative z-score indicates that the value is below the mean.

So, the 34 week gestation's period baby weighs 0.11 standard deviations below the mean.

Babies born after a gestations period of 40 weeks have a mean weight of 3400 grams and a standard deviation of 425 grams. A 40-week gestation period baby weighs 3300 grams.

Here, we have $\mu = 3400, \sigma = 425, X = 3300$

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

$Z = \frac{3300- 3400}{425}$

$Z = -0.24$

So, the 41 week gestation's period baby weighs 0.24 standard deviations below the mean.

Which baby weighs relatively less?

A. The baby born in week 40 does since its z-score is smaller.