Answer
a) $0.4129$
b) $25$
c) $19$
d) They need to be updated.
Work Step by Step
a) We first find the $z$-score:
$z=\frac{174−182.9}{40.8}=−0.22$
Using the table of $z$-scores, we see that this corresponds to $0.4129.$
b) The number is:
$\frac{3500}{140}=25$
c) The new number with the new mean is:
$\frac{3500}{182.9}=19$
d) It is necessary to review safety regulations because the ability of the boats as well as the mean weight of people changes over time.
