Children can accurately predict the gender of a person stereotypically based on the attributes associated with particular activities at around the age of five. This is when children typically develop a basic understanding of gender roles and stereotypes. Let's explore this further:

1. Development of Gender Identity:
- At a very young age, children start to develop a sense of their own gender identity and become aware of the differences between boys and girls.
- Around the age of two, children begin to categorize themselves and others based on gender, often using physical characteristics such as clothing and hairstyles.
- By the age of five, children have a more solidified gender identity and a better understanding of societal expectations and stereotypes associated with gender roles.

2. Formation of Gender Stereotypes:
- As children grow older, they start to form stereotypes about gender roles and the activities typically associated with each gender.
- Society often reinforces these stereotypes through media, toys, and social interactions.
- For example, children may associate activities like playing with dolls or cooking with girls, while activities like playing with cars or sports may be associated with boys.

3. Understanding Gendered Attributes:
- Around the age of five, children begin to understand and associate certain attributes with gender, based on societal norms and expectations.
- They may perceive certain characteristics, such as long hair or wearing dresses, as more feminine, while associating traits like strength or rough play with masculinity.

4. Accuracy of Predicting Gender Stereotypically:
- At this age, children are able to make more accurate predictions about a person's gender based on stereotypical attributes associated with activities.
- They may assume that someone engaged in activities like playing with dolls or wearing makeup is likely a girl, while someone involved in activities like playing with trucks or climbing trees is likely a boy.
- However, it's important to note that these predictions are based on societal stereotypes and may not always reflect an individual's actual gender identity or interests.

In conclusion, children around the age of five can accurately predict the gender of a person based on stereotypical attributes associated with particular activities. Their understanding of gender roles and stereotypes develops as they grow older and become more aware of societal expectations.