Question

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

Answer 1

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 $\mu=$38 mmHg and $\sigma=$ 9 mmHg.

If we take a random sample n= 25 newborns, then  using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$, we have

At x= 36

$z=\dfrac{36-38}{\dfrac{9}{\sqrt{25}}}\approx-1.11$

At x= 41

$z=\dfrac{36-38}{\dfrac{9}{\sqrt{25}}}\approx1.67$

Using table for z-values, the probability that the sample mean will be greater than 36 :

$P(z>-1.11)=1-P(\leq-1.11)=1-(1-P(z\leq1.11))=P(z\leq1.11)=0.8665004\approx0.8665$

The probability that the sample mean will be between 36 and 41 :-

$P(-1.11$