x=oxygen taken by athletes in milliliters per kilogram
x~Normal
a) he probability that an elite athlete has a maximum oxygen uptake of at least 60 ml/kg
x=P(Atleast 60)
= P(X > 60)
= P(z > (60 - 80)/9.2)
= P(z > -2.173)
=1-P(Z<2.173)
=1-0.01485
= 0.9851
b)
P(65or lower)
= P(X < 65)
= P(z (65 - 80)/9.2)
= P(z < -1.63)
= 0.0515
#P(X < 65)=0.0515
c)Consider someone with a maximum oxygen uptake of 22 ml/kg
to find
P(X<22)=
= P(z (22 - 80)/9.2)
= P(z < -6.3043)
= 1.4470*E-10~0
the probability is approximately 0
Hence,
It is not likely that this person is an elite athlete because the probability is less than 0.05
Ans: No
#P(X < 65)=0.0515
(d) here we want to find x suh that top of 20%
ie P(X>x)=0.20
P(X<x)=1-0.20=0.80
For 80th percentile, we look for the value closest to 0.80 in
standard normal table which is
z-score corresponding to 80% = 0.84
x=80+9.2(0.84)=20.163
x=87.74
#maximum oxygen uptake top 20% is 87.74
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