Question

Newborn males have weights with a mean of 3272.8 g and a standard deviation of 660.2 g. Newborn females have weights with a mean of 3037.1 g and a standard deviation of 706.3 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1500 g or a female who weighs 1500 g?

Answer 1

The correct option is:   a female who weighs 1500 g

Explanation

Formula for finding the z-score is:  $z= \frac{X-\mu}{\sigma}$

Newborn males have weights with a mean$(\mu)$ of 3272.8 g and a standard deviation$(\sigma)$ of 660.2 g.

So, the z-score for the newborn male who weighs 1500 g will be.......

$z(X=1500)=\frac{1500-3272.8}{660.2}=-2.685... \approx -2.69$

According to the normal distribution table,  $P(z=-2.69)=0.0036 = 0.36\%$

Now, newborn females have weights with a mean$(\mu)$ of 3037.1 g and a standard deviation$(\sigma)$ of 706.3 g.

So, the z-score for the newborn female who weighs 1500 g will be.......

$z(X=1500)=\frac{1500-3037.1}{706.3}=-2.176... \approx -2.18$

According to the normal distribution table,  $P(z=-2.18)=0.0146 = 1.46\%$

As we can see that the probability that a newborn female has weight of 1500 g is greater than newborn male,  so a newborn female has the weight of 1500 g that is more extreme relative to the group from which he came.