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

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=(x-\mu)/((\sigma)/(√(n)))`, we have

At x= 36

`z=(36-38)/((9)/(√(25)))\approx-1.11`

At x= 41

`z=(36-38)/((9)/(√(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<z<1.67)=P(z<1.67)-P(z<-1.11)\\\\=0.9525403-0.1334995\\\\=0.8190408\approx0.8190`