Question

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 σ = 0.5 liters, while among female smokers in the same age group, FEV is normally distributed with a mean µ= 3.3 liters and standard deviation σ = 0.6 liters.

(a) 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?

(b) 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 non-smoker in the above age group has impaired lung function?

Answer 1

the FEV among female non-smokers has  µ= 4 , standard deviation σ = 0.5

the FEV among female smokers has  µ= 3.3 , standard deviation σ = 0.6

since both are normally distributed

a ) P (x 2.5) = = = 0.0013

the probability that a female smoker in the above age group has impaired lung function is 0.0013

b )

the probability that a female non-smoker in the above age group has impaired lung function=0.0918