Respuesta :
Answer:
[tex] P(z> \frac{(69.3-64)-0}{\sqrt{2.74^2 +2.7^2}}) =P(z>1.38)[/tex]
and we can find this probability using the complement rule and we got:
[tex] P(z>1.38)=1-P(z<1.38) = 1-0.9162= 0.0838[/tex]
So then we can conclude that approximately 8.38% of the men are taller than women
Step-by-step explanation:
Let X the random variable who represent the heights of women aged 20 to 29 and the distribution is given by:
[tex] X \sim N(64, 2.74)[/tex]
And let Y the heights of men aged 20 to 29 and the distribution for Y is given by:
[tex] Y \sim N(69.3, 2.7)[/tex]
And for this case we want to find the following probability:
[tex] P(Y>X) = P(Y-X >0)[/tex]
The distribution for Y-X is given by:
[tex] Y-X \sim N (\mu_Y -\mu_X , \sqrt{\sigma^2_Y +\sigma^2_X})[/tex]
We can define the random variable Z= Y-X and the we can use the z score formula given by:
[tex] z =\frac{z -\mu_z}{\sigma_z}[/tex]
And using the z score formula we got:
[tex] P(z> \frac{(69.3-64)-0}{\sqrt{2.74^2 +2.7^2}}) =P(z>1.38)[/tex]
and we can find this probability using the complement rule and we got:
[tex] P(z>1.38)=1-P(z<1.38) = 1-0.9162= 0.0838[/tex]
So then we can conclude that approximately 8.38% of the men are taller than women
