SOLUTION: The heights of a group of athletes are modelled by a normal distribution with mean 180 cm and standard deviation 5.2 cm. The weights of this group of athletes are modelled by a nor

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Question 383834: The heights of a group of athletes are modelled by a normal distribution with mean 180 cm and standard deviation 5.2 cm. The weights of this group of athletes are modelled by a normal distribution with mean 85 kg and standard deviation 7.1 kg.
Find the probability that a randomly chosen athlete.
a. is taller than 188 cm.
b. weighs less than 97 kg
c. Assuming that for these athletes height and weight are independent, find the probability that a randomly chosen athlete is taller than 188 cm and weighs more than 97 kg.
d. Comment on the assumption that height and weight are independent.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. P%28H+%3E+188%29+=+P%28%28H+-+181%29%2F5.2+%3E+%28188+-+181%29%2F5.2+=+1.346%29. Hence P(H > 188) = P(Z > 1.346) = 0.0885.
b. P%28W+%3C+97%29+=+P%28%28W+-+85%29%2F7.1+%3C+%2897+-+85%29%2F7.1+=+1.69%29. Hence P(W < 97) = P(Z < 1.69) = 0.9545.
c. The probability that a randomly chosen athlete is taller than 188 cm and weighs more than 97 kg = (0.0885)*(1- 0.9545) = 0.0885*0.0455 = 0.00402675, assuming independence of height and weight.
d. Although the assumption of independence may be valid, it may not be entirely realistic, as taller people in general tend to be heavier than shorter people, i.e., there is some sort of positive correlation between height and weight. (Just my opinion.)