Respuesta :
Answer:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
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:
[tex] z= \frac{33.2-34.5}{1.3}= -1[/tex]
And for the case of Sue we got:
[tex] z = \frac{32.7-33.9}{1.2}= -1[/tex]
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:
[tex]X\sim N(\mu = 34.5, \sigma=1.3)[/tex]
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:
[tex]Y\sim N(\mu = 33.9, \sigma=1.2)[/tex]
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:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
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:
[tex] z= \frac{33.2-34.5}{1.3}= -1[/tex]
And for the case of Sue we got:
[tex] z = \frac{32.7-33.9}{1.2}= -1[/tex]
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.
