Answer
a) $140$
b) $.9999$
c) $0.8078$
d)No
Work Step by Step
a)mean weight:
$\frac{3500}{25}=140$ Ibs
b)z-score:
$z=\frac{(140)−(182.9)}{40.8/(\sqrt{25})}=−5.257$
This is less than $-3.5$, hence the probability is $0.9999$.
c) z-score:
$z=\frac{175−182.9}{40.8/\sqrt{20}}=−0.87$
Consulting the table of $z$-scores, we see that the probability is $0.8078$.
d) No, this is still not safe. A much higher probability is required for safety regulations.
