Employer made a mistake, overstating the number of weeks of severance pay that I will be receiving.

I was notified that my position will be eliminated in the coming few months. I had a very short informal meeting with an HR rep where the rep explained to me the number of weeks of severance pay to expect and other information about Cobra, etc. The rep then wrote down manually the information on a custom human resources notepad where the company's logo, the company's address, the name, and the position of the HR person were printed. The hand written part displays the notification date, end date, date when my severance begins and the number of weeks of severance pay. There was no signature on it. I was told that I will receive the formal severance package on my notification date. Since then, I read the company's severance calculation rules and I realized that the HR person made a mistake and overstated the number of weeks by double. Based on this promise, do I have a legal right to request that the company honor the quoted number of weeks of severance pay? If so, how would I go about doing that?