Q:

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 mean of 38 mmHg and astandard deviation of 9 mmHg. If we take a random sample of 25newborns what is the probability that the sample meana) will be greater than 36b) will be between 36 and 41

Accepted Solution

A:
Answer: a) 0.8665b) 0.8190Step-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 haveAt 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]