Answer:
![z = \frac{X -\mu}{\sigma}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%7D)
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](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B33.2-34.5%7D%7B1.3%7D%3D%20-1)
And for the case of Sue we got:
![z = \frac{32.7-33.9}{1.2}= -1](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B32.7-33.9%7D%7B1.2%7D%3D%20-1)
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)](https://tex.z-dn.net/?f=X%5Csim%20N%28%5Cmu%20%3D%2034.5%2C%20%5Csigma%3D1.3%29)
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)](https://tex.z-dn.net/?f=Y%5Csim%20N%28%5Cmu%20%3D%2033.9%2C%20%5Csigma%3D1.2%29)
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}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%7D)
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](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B33.2-34.5%7D%7B1.3%7D%3D%20-1)
And for the case of Sue we got:
![z = \frac{32.7-33.9}{1.2}= -1](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B32.7-33.9%7D%7B1.2%7D%3D%20-1)
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.