I'm assuming this question is coming from a statisitcs homework assignment.
You'll want to look-up at probability under a normal distribution,
Given a random variable (for example nominal weight), if that random variable is described by a normal distribution, then the mean and standard deviation is all you need to calculate confidence intervals and the probability of specific weight ranges occurring in the population.
I gave a link to the Wikipedia article for completeness, but there's great resources online and YouTube (kahn academy is a nice resource) to walk you through how the normal distribution works, calculating the probability of specific values occurring, dealing with estimating the shape of a normally distributed variable and much more.