Question

Use z scores to compare the given values. Based on sample​ data, newborn males have weights with a mean of 3206.5 g and a standard deviation of 724.6 g. Newborn females have weights with a mean of 3024.5 g and a standard deviation of 505.3 g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1700 g or a female who weighs 1700 ​g? Since the z score for the male is zequals nothing and the z score for the female is zequals nothing​, the ▼ female male has the weight that is more extreme. ​(Round to two decimal​ places.)

Answer 1

Answer:

Since the z score for the male is z = -2.08 and the z score for the female is z = -2.62, the female has the weight that is more extreme.

Step-by-step explanation:

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.

In this problem, we have that:

Whoever's z-score has the higher absolute value has the weight that is more extreme relative to the group.

Male who weighs 1700 g

Based on sample​ data, newborn males have weights with a mean of 3206.5 g and a standard deviation of 724.6 g.

This means that $\mu = 3206.5, \sigma = 724.6$

So

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

$Z = \frac{1700 - 3206.5}{724.6}$

$Z = -2.08$

The absolute value of the zscore is 2.08

Female who weighs 1700 ​g

Newborn females have weights with a mean of 3024.5 g and a standard deviation of 505.3 g.

This means that $\mu = 3024.5, \sigma = 505.3$

So

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

$Z = \frac{1700 - 3024.5}{505.3}$

$Z = -2.62$

The absolute value of the zscore is 2.62.

So the female has the more extreme weight.

Since the z score for the male is z = -2.08 and the z score for the female is z = -2.62, the female has the weight that is more extreme.