Answer
a) $0.57$
b) $0.998$, yes
Work Step by Step
a) We must find the probability that the weight of the man exceeds $175$ pounds:
Hence, we find z:
$z=\frac{175−182.9}{40.9}=−0.19$
Thus, using the table of z-scores, we can find that the corresponding probability is: $1−0.4286=0.57$.
b) We find z:
$z=\frac{175−182.9}{40.9/\sqrt{213}}=−0.19$
Thus, using the table of z-scores, we can find that the corresponding probability is $1-0.002=0.998$.
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.
