In the university library elevator there is a sign...

In the university library elevator, there is a sign indicating a 16-person limit as well as a weight limit of 2500 pounds. Suppose that the weight of students, faculty, and staff is approximately normally distributed with a mean weight of 150 pounds and a standard deviation of 27 pounds. When the elevator is full, we can think of the 16 people in the elevator as a simple random sample of people on campus. What average weight for these 16 people in the elevator will result in the total weight exceeding the weight limit of 2500 pounds? * Please round to two decimal places.

Transcript

00:01 So this question actually ends up being a very simple question, but i'll expand upon it.

00:07 For individual people, we are assuming that we have a normal distribution with the weight centered at 150 pounds and a standard deviation of 27 pounds.

00:18 And you have 16 people and it says that the load limit is 2 ,500 pounds.

00:28 And your question says, what would the average weight have to be in order for it to exceed 2 ,500 pounds? and it says give two decimals.

00:38 Well, if i take 2 ,500 pounds and divide it by the 16 people, i find out that that comes out to be 156 .255 pounds.

00:50 So if the average weight is more than that, we will exceed 2 ,500 pounds.

00:56 Now, probably a better question is how likely is it? what is the probability of getting that total to be more than 2 ,500 pounds? and so what's the probability people get on and you're over the weight? that would be the better question, but the average would be this.

01:18 And so i think that's all you need.

01:20 But i'll do this, and we can do one of two things.

01:24 We can either find the distribution for 16.

01:28 This is 16 people added together.

01:32 So this is for a total of 16 people.

01:35 And that mean would be 150 times 16.

01:39 And 150 times 16 would be the total would end up being 2 ,400.

01:45 Now, the standard deviation, that's a little more tricky.

01:48 Because we would take each of these people's variance, 27 squared, plus 27...