Forced expiratory volume (FEV) is an index of pulmonary function that measures the volume of air expelled after 1 second of constant effort. 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 = 0.5 L. In comparably aged currently smoking men FEV is nor- mally distributed, with mean = 3.5 L and standard deviation = 0.6 L. 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 has functional impairment?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Forced expiratory volume (FEV) is an index of pulmonary
function that measures the volume of air expelled after 1
second of constant effort. FEV is influenced by age, sex,
and cigarette smoking. Assume that in 45- to 54-year-old
nonsmoking men FEV is
4.0 L and standard deviation = 0.5 L.
In comparably aged currently smoking men FEV is nor-
mally distributed, with mean = 3.5 L and standard deviation
= 0.6 L.
If an FEV of less than 2.5 L is regarded as showing
some
inability to climb stairs, etc.), then what is the probability
that a currently smoking man has functional impairment?
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