An elevator has a placard stating that the maximum capacity is $4500lb-29$ passengers. So$,29$ adult male passengers can have a mean weight of up to $\frac{4500}{29}=155$ pounds. Assume that weights of males are normally distributed with a mean of $178lb$ and a standard deviation of $32lb.$

a$.$ Find the probability that $1$ randomly selected adult male has a weight greater than $155lb.$

b$.$ Find the probability that a sample of $29$ randomly selected adult males has a mean weight greater than $155lb.$

c$.$ What do you conclude about the safety of this elevator?

a$.$ The probability that $1$ randomly selected adult male has a weight greater than $155lb$ is $($Round to four decimal places as needed.$)$

b$.$ The probability that a sample of $29$ randomly selected adult males has a mean weight greater than $155lb$ is $($Round to four decimal places as needed.$)$

c$.$ Does this elevator appear to be safe?

A$.$ No$,$ because $29$ randomly selected people will never be under the weight limit$.$

B$.$ Yes, because $29$ randomly selected adult male passengers will always be under the weight limit$.$

C$.$ No$,$ because there is a good chance that $29$ randomly selected adult male passengers will exceed the elevator capacity.

D$.$ Yes, because there is a good chance that $29$ randomly selected people will not exceed the elevator capacity.