SOLUTION: The physical fitness of a patient is often measured by the patient’s maximum oxygen uptake (ml/kg). The mean maximum oxygen uptake for cardiac patients who regularly participate in

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Question 667827: The physical fitness of a patient is often measured by the patient’s maximum oxygen uptake (ml/kg). The mean maximum oxygen uptake for cardiac patients who regularly participate in sports or exercise programs is 24.1 ml/kg and the standard deviation is 6.30 ml/kg. Maximum oxygen uptake measurements have a Normal distribution.
a) What is the probability that a cardiac patient who regularly participates in sports or exercise programs has a maximum oxygen uptake of at least 20 ml/kg?
b) What is the probability that a cardiac patient who regularly participates in sports or exercise programs has a maximum oxygen uptake between 18 ml/kg and 31 ml/kg?
c) What is the probability that a cardiac patient who regularly participates in sports or exercise programs has a maximum oxygen uptake of 10.5 ml/kg or lower?
d) Consider a cardiac patient with a maximum oxygen uptake of 10.5 ml/kg. Is it likely that this patient regularly participates in sports or exercise programs?

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

μ = 24.1  and  σ = 6.3

I.Find the corresponding z-values: z = (x-24.1)/6.3 

II.  Use that z-value to calculate the P-value asked for

corresponding P-value will be the portion of under the standard normal curve

to the LEFT of the z-value

a) P(x≥20) = 1 - P(z-value)

b)P( 18< x< 31) = P(z=7.1/6.3)- P(z = -6.1/6.3)  

c) P(x ≤ 10.5) = P(z = -13.6/6.3)

d) z-value =  -2.1587,  most likely NOT :)

Important to Understand z -values as they relate to the Standard Normal curve:

Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Note: z = 0 , 50% of the area under the curve is to the left and 50%  to the right