Final answer:
Cooked chicken should be used within 3 to 4 days; thus, chicken salad made with chicken grilled on July 20th should be served or discarded by July 24th to avoid foodborne illness.
Step-by-step explanation:
The question you have asked is related to food safety and shelf life management of perishable food items. It is generally recommended that cooked chicken, like what would be in your chicken salad, be consumed or stored in the refrigerator within 2 hours of cooking and used within 3 to 4 days. If the chicken was grilled on July 20th, the chicken salad should be served or discarded by July 24th to reduce the risk of foodborne illness.
In the case provided, where the microbiology department experienced sickness after a picnic, it highlights the importance of proper food handling and prompt refrigerator storage to prevent contamination and growth of bacteria which can cause food poisoning.