Answer
a. .57 b. .998; yes
Work Step by Step
a) We must find the probability that the weight of the man exceeds 175 pounds:
We use the z-score to find:
$z=\frac{175-182.9}{40.9}=-.19$
Thus, using the table of z-scores, we find that this corresponds to a probability of $1-.4286=.57$
b) $z=\frac{175-182.9}{40.9/\sqrt{213}}=-2.8$
Thus, using the table of z-scores, we find that this corresponds to a probability of $1-.002=.998$
Yes, the pilot should be worried about this weight. After all, planes are dangerous if they are overweight, so there needs to be an even lower probability for the pilot to feel safe.
