Question

An elevator can safely hold 3,500 lbs. A sign in the elevator limits the passenger count to 15. If the adult population has a mean weight of 180 lbs with a 25 lbs standard deviation, how unusual would it be, if the central limit theorem applied, that an elevator holding 15 people would be carrying more than 3,500 pounds?

I put the following in R: pnorm(3500/15, mean=180,sd = 25/sqrt(15),lower.tail=FALSE) what will be my next step?

Answer 1

We know that the sum of the normal random variables is also a random variable. Thus, for sum of 15 people's weight, we can say that:

Cumulative mean, = 15*180

= 2700

Cumulative std. deviations = * 25

= 96.825

So, we need to find:

P(X>3500) = P(Z>(3500-2700)/96.825)

= P(Z>8.262)

= ~ 0

In R you can do this also as:

pnorm(3500/15, mean=180,sd = 25/sqrt(15), lower.tail=FALSE)

you just need to run this program and it will give you a probability very close to 0

Since it is < 0.05, we can say that it will be a very unusual event.

Please upvote if you have liked my answer, would be of great help. Thank you.