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.
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?
The Attempt at a Solution
I know that the mean for decline is going to be 0.9L and the standard deviation will be 0.6L because n=30 but I do not know where to go from there.