Question

According to the World Health Organization (WHO) Child Growth Standards, the head circumference for boys at birth is normally distributed with a mean of 34.5cm and a standard deviation of 1.3cm. For girls, the mean is 33.9cm with a standard deviation of 1.2cm. Eddie and Sue are twins. Eddie was born with a head circumference of 33.2cm and Sue was born with a head circumference of 32.7cm.
Which child's head circumference is smaller relative to other children of the same sex?

A.Eddie

B.Sue

C.They are the same size relative to other children of the same sex.

Answer 1

Answer:

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

This z score tell to us how many deviations we are below or above the mean for a given normal distribution.

For the case of Eddie we got:

$z= \frac{33.2-34.5}{1.3}= -1$

And for the case of Sue we got:

$z = \frac{32.7-33.9}{1.2}= -1$

So then for both cases we see that Eddie and Sue are 1 deviation below the true mean for each gender so then the best conclusion for this case would be:

C.They are the same size relative to other children of the same sex.

Step-by-step explanation:

We can define the random variable X as the head circumference for boys at birth and we know that the distribution for X is given by:

$X\sim N(\mu = 34.5, \sigma=1.3)$

Similarly we can define the random variable Y as the head circumference for boys at birth and we know that the distribution for Y is given by:

$Y\sim N(\mu = 33.9, \sigma=1.2)$

And we know that Eddie was born with 33.2 cm and Sue with 32.7 cm for the head circumference . Since we are interested to determine which child's head circumference is smaller relative to other children of the same sex, we can use the z score formula given by this formula:

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

This z score tell to us how many deviations we are below or above the mean for a given normal distribution.

For the case of Eddie we got:

$z= \frac{33.2-34.5}{1.3}= -1$

And for the case of Sue we got:

$z = \frac{32.7-33.9}{1.2}= -1$

So then for both cases we see that Eddie and Sue are 1 deviation below the true mean for each gender so then the best conclusion for this case would be:

C.They are the same size relative to other children of the same sex.