Question 2: An important indicator of lung function is forced expiratory volume

Question

Question 2: An important indicator of lung function is forced expiratory volume (FEV), which is the volume of air that a person can expire in one second. Dr. Jones plans to measure FEV in a random sample of n young women from a certain population, and to use the sample mean (y) as an estimate of the population mean. Let A represent the event that Jones's sample mean will be within ± 100 of the true population mean. Assume that the population distribution is normal with mean 3,000 mLi and standard deviation 400 mld (a) Find Prob(A) if n 15 (b) Find Prob(A) ifn -60+ (c) How does Prob(A) depend on the sample size? That is, as n increases, does Prob(A) increase, decrease or stay the same?

Explanation / Answer

a)here std error of mean =std deviation/(n)1/2 =400*(15)1/2 =103.2796

therefore P(3000-100<X<3000+100)=P(-100/103.2796<Z<100/103.2796)=P(-0.9682<Z<0.9682)=0.8335-0.1664

=0.6671

b)

std error of mean =std deviation/(n)1/2 =400*(60)1/2 =51.6398

therefore P(3000-100<X<3000+100)=P(-100/51.6398<Z<100/51.6398)=P(-1.9365<Z<1.9365)=0.9736-0.0264

=0.9472

c)from above as sample size increase P(A) also increases.

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