Question

Your class has to line up according to birthdays to complete an activity, and you discover that of the 35 people in the class, four of them have the same birthday. You want to find out if this is unusual, so you conduct a simulation and repeat it 50 times to see how many times 4 people have the same birthday. The results are shown in the dot plot. Is your class unusual? Explain.

A) The class is not unusual. You cannot use a simulation to see if experimental results are typical.
B) The class is unusual. None of the simulations had four people with the same birthday.
C) The class is not unusual. There were a few simulations where four people had the same birthdays.
D) The class is unusual. Even though there were a few simulations with four people having the same birthday, the majority did not.

Answer 1

The class with four students sharing the same birthday is considered unusual if the simulation shows that such an event is not common. Statistics and probability theory are used to analyze these situations, and graphical representations such as dot plots help visualize data. The Central Limit Theorem suggests distributions become more normal as sample sizes increase.

Step-by-step explanation:

In the context of the initial scenario where a class of 35 students has four people with the same birthday, and after conducting a simulation 50 times to test the likelihood of this occurrence, the findings of the simulation are crucial to determine if the situation is unusual or not. If in none of the 50 simulations did four people have the same birthday, then the class appears to be unusual in this respect. However, if there were a few simulations where four people shared the same birthday, it may indicate that while rare, such an event is not impossible and can occur by chance, meaning the class may not be as unusual. The subject of statistics and probability theory are essential in understanding these concepts. Creating and analyzing graphical representations like dot plots and bar graphs also aids in visualizing and interpreting such data.

To apply this analysis practically, one could also examine the probability of students carrying change, having ridden a bus recently, or having a certain number of siblings. Additionally, the concept of the Central Limit Theorem is demonstrated when observing the distribution of sample means obtained from rolling varying numbers of dice, where the distribution tends towards normal distribution as the number of dice increases.