Respuesta :
Answer:
[tex] P(42 < \bar X <48)[/tex]
And we can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z scores for the limits of the interval we got:
[tex] z= \frac{42-44}{\frac{35}{\sqrt{59}}}= -0.4[/tex]
[tex] z= \frac{48-44}{\frac{35}{\sqrt{59}}}= 0.878[/tex]
And we want to find this probability:
[tex] P(-0.4<z<0.878)[/tex]
And we can use the foolowing excel command and we got:
=NORM.DIST(0.878;0;1;TRUE)-NORM.DIST(-0.4;0;1;TRUE)
And we got:
[tex] P(-0.4<z<0.878)=0.4655[/tex]
Step-by-step explanation:
For this case we know the following parameters:
[tex] \mu = 44 ,\sigma =35[/tex]
We select a sample size of n =59. So then the sample size is large enough to use the central limit theorem and the distribution for the sample mean is given by:
[tex] \bar X \sim N(\mu \frac{\sigma}{\sqrt{n}})[/tex]
We want to find the following probability:
[tex] P(42 < \bar X <48)[/tex]
And we can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z scores for the limits of the interval we got:
[tex] z= \frac{42-44}{\frac{35}{\sqrt{59}}}= -0.4[/tex]
[tex] z= \frac{48-44}{\frac{35}{\sqrt{59}}}= 0.878[/tex]
And we want to find this probability:
[tex] P(-0.4<z<0.878)[/tex]
And we can use the foolowing excel command and we got:
=NORM.DIST(0.878;0;1;TRUE)-NORM.DIST(-0.4;0;1;TRUE)
And we got:
[tex] P(-0.4<z<0.878)=0.4655[/tex]
