Stuck at an exercise

[Naethiel]

I need help with this homework. Even just some indication on how to begin would be much appreciated.

The problem is:
There's an elevator with a maximum amount of load of 3000kg. The population of people that use the elevator has an average weight of 81kg and standard deviation of 15kg. For a sample of 36 people from this population, count the probability of their total weight being higher than 3000 kg.

 

[Dr.Peterson]

I need help with this homework. Even just some indication on how to begin would be much appreciated.

The problem is:
There's an elevator with a maximum amount of load of 3000kg. The population of people that use the elevator has an average weight of 81kg and standard deviation of 15kg. For a sample of 36 people from this population, count the probability of their total weight being higher than 3000 kg.

Presumably you have learned something about the normal distribution, and specifically about the sampling distribution of sample means. (If not, look up those terms.)

If their total weight is greater than 3000 kg, what can you say about their mean weight?

What are the mean and standard deviation of the distribution of sample means, given what you are told about the population and the sample size?

Please show us whatever you can, using these ideas, or at least show an example you were given involving these ideas, so we can be sure what you are learning.

 

[Naethiel]

this is my try , sorry for the delay didn't have much time, im not sure if what ive done here is correct or completely wrong, if its the latter some more help would be much appreciated.

 

[Dr.Peterson]

Without going through all the details, that looks like the right work.

Clearly you know more than you let on initially!