Question: Forced expiratory volume (FEV) is an index of pulmonary function

Forced expiratory volume (FEV) is an index of pulmonary function that measures the volume of air expelled after 1 second. FEV is influenced by age, sex and cigarette smoking. Assume that in 45- to 54-year-old nonsmoking men FEV is normally distributed with mean = 4.0 L and standard deviation = 0.5L.

But for 45- to 54-year-old smoking men FEV is normally distributed, with mean 3.5 L and standard deviation = 0.6 L.

(a) If an FEV of less than 2.5 L is regarded as showing some functional impairment (occasional breathlessness, inability to climb stairs, etc.), then what is the probability that a currently smoking man in the 45- to 54-age group has functional impairment?

 (Use 4 decimal places.)

(b) Some people are not functionally impaired now, but their pulmonary function usually declines with age and they eventually will be functionally impaired. Assume that the decline in FEV over n years is normally distributed, with mean = 0.03n L and standard deviation = 0.02n L. What is the probability that a 45-year-old non-smoking man with an FEV of 4.0 L will be functionally impaired by age 75?

HINT: If a 45 year old man has FEV = 4.0, then he will be functionally impaired at age 75 years if his FEV has dropped at least 1.5 (from age 45 to age 75). The drop in FEV is a normally distributed random variable with mean 0.03n where n = # years for the drop to occur. In this problem, n = 75-45=30. The standard deviation is given as 0.02n using the same value for n.

 (Use 4 decimal places.)

(c) What is the probability that a 45-year-old smoking man with an FEV of 3.5 L will be functionally impaired by age 75?

 (Use 4 decimal places.)

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