Don't understand question

The weight of a large herd of goats was found to have a distribution that is approximately normal with mean 70.8 kg and standard deviation 6.4 kg. What is the probability that the sum of their weights is less than 145 kg?

Do I use cumulative probability? I don't know how to get a probability of a sum of values.

Re: Don't understand question

Hey yvonnehr.

Recall that the sum of normal distributions is a normal distribution where the final variance is the sum of all individual variances (if they are all independent) and the mean is the sum of all the means.

If you have n independent observations with variance sigma^2 and mean mu then the sum will be distributed Normal(n*mu,n*sigma^2) which means you can use this to calculate a probability of the sum of the weights.

Re: Don't understand question

Hi Chiro. Thank you for your reply.

Do I need n, the number of trials or individuals, to calculate this?

Re: Don't understand question

Yes you need some value for n if you want to make a specific calculation.