We are given normally distributed body weights with a mean of $195$ lbs. and a standard deviation of $24$ lbs. If an elevator in town has a maximum capacity of $20$ persons and a rated maximum weight of $4100$ lbs., what is the probability that the elevator, when filled to capacity, will not exceed its rated weight? (in other words, what is the probability that a sample of $20$ citizens will have a mean weight of less than $205$ lbs.?)
This is how I thought the problem was to be worked
$$205-195=24/\sqrt{20}=1.862$$ which of course is not correct.