Answer
a) $0.6517$
b) $0.9115$
c) Should be reduced.
Work Step by Step
a) We use the z-score to find:
$z=\frac{167−182.9}{40.8}=−0.39$
Hence, using the table of z-scores, we find that this corresponds to a probability of $1−0.3483=0.6517$
b) We use the z-score to find:
$z=\frac{167−182.9}{40.8/\sqrt{12}}=−1.35$
Thus, using the table of z-scores, we find that this corresponds to a probability of $1−0.0885=0.9115$
c) For safety standards, the probability is too low, hence the weight limit should be reduced.