Forced Expiratory Volume FEV is an index of lung function th

Forced Expiratory Volume (FEV) is an index of lung function that measures the volume of air expelled after 1 second of constant effort. Suppose that in females aged 40-55 years, the FEV among non-smokers is normally distributed with a mean µ= 4 liters and standard deviation = 0.49 liters, while among female smokers in the same age group, FEV is normally distributed with a mean µ= 3.3 liters and standard deviation = 0.56 liters.

1A. If an FEV of 2.5 liters or lower is regarded as an indicator of impaired lung function, then what is the probability that a female smoker in the above age group has impaired lung function?

1B. Using the same FEV criteria as in #1a, what proportion of female non-smokers have impaired lung function?

Solution

Normal Distribution
Mean ( u ) =4
Standard Deviation ( sd )=0.49
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 2.5) = (2.5-4)/0.49
= -1.5/0.49 = -3.0612
= P ( Z >-3.061) From Standard Normal Table
= 0.9989                  
P(X < = 2.5) = (1 - P(X > 2.5)
= 1 - 0.9989 = 0.0011                  
b)

Mean ( u ) =3.3
Standard Deviation ( sd )=0.56
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 2.5) = (2.5-3.3)/0.56
= -0.8/0.56 = -1.4286
= P ( Z >-1.429) From Standard Normal Table
= 0.9234                  
P(X < = 2.5) = (1 - P(X > 2.5)
= 1 - 0.9234 = 0.0766