Answer: a) 0.8665
b) 0.8190
Step-by-step explanation:
Given : The partial pressure of oxygen PaO2 is a measure ofthe amount of oxygen in the blood. Assume that the distribution ofPaO2 levels among newborns has a [tex]\mu=[/tex]38 mmHg and [tex]\sigma=[/tex] 9 mmHg.
If we take a random sample n= 25 newborns, then using formula [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex], we have
At x= 36
[tex]z=\dfrac{36-38}{\dfrac{9}{\sqrt{25}}}\approx-1.11[/tex]
At x= 41
[tex]z=\dfrac{36-38}{\dfrac{9}{\sqrt{25}}}\approx1.67[/tex]
Using table for z-values, the probability that the sample mean will be greater than 36 :
[tex]P(z>-1.11)=1-P(\leq-1.11)=1-(1-P(z\leq1.11))=P(z\leq1.11)=0.8665004\approx0.8665[/tex]
The probability that the sample mean will be between 36 and 41 :-
[tex]P(-1.11<z<1.67)=P(z<1.67)-P(z<-1.11)\\\\=0.9525403-0.1334995\\\\=0.8190408\approx0.8190[/tex]
