Question

Force expiratory volume (FEV) is an index of pulmonary function that measures the volume of air expelled after 1 second of constant effort. FEV is known to be influenced by age, sex and cigarette smoking. Assume that in 45-54 year-old smoking males, FEV is normally distributed with mean j = 3 liters and standard deviation o = 0.7 liters. For the following, report probabilities between 0 and 1; round all answers to 4 decimal places. a. If a FEV of less than 2.3 liters is regarded as showing some functional impairment (occasional breathlessness, inability to climb stairs, etc.), then what is the probability that a 45- 54 year-old currently smoking male has functional impairment? b. Suppose the average FEV for 45-54 year-old NON-smoking males is 4 liters. What is the probability that a 45-54 year-old currently-smoking male will have FEV greater than 4 liters? c. With a random sample of two (2) 45-54 year-old currently-smoking males, what is the probability that at least one of them has functional impairment? d. How low would the FEV a 45-54 year-old currently smoking male need to be in order to be in the bottom 20 % of the distribution of FEV?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	3
std deviation   =σ=	0.7

a)

probability =P(X<2.3)=(Z<(2.3-3)/0.7)=P(Z<-1)=0.1587

b)

probability =P(X>4)=P(Z>(4-3)/0.7)=P(Z>1.43)=1-P(Z<1.43)=1-0.9236=0.0766

(please try 0.0764 if this comes wrong)

c)

P(at least one) =1-P(none) =1-(1-0.1587)*(1-0.1587)=0.2922

d)

for 20th percentile critical value of z=		-0.84
therefore corresponding value=mean+z*std deviation=			2.4109