The Number Of Absences For One Week For All Students At A High School Was Compiled, And The Probability Distribution Below Was Created. What Is The Probability In Any Given Week That A Randomly Selected Student Will Be Absent No More Than One
**The number of absences for one week for all students at a high school was compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one time?**
Probability Distribution:
| Number of Absences | Probability |
|---|---|
| 0 | 0.2 |
| 1 | 0.5 |
| 2 | 0.2 |
| 3 | 0.05 |
| 4 | 0.05 |
| 5 | 0.05 |
Understanding the Problem
To find the probability that a randomly selected student will be absent no more than one time, we need to consider the probability distribution provided. The distribution shows the number of absences and their corresponding probabilities.
Step 1: Identify the Relevant Probabilities
We are interested in finding the probability of a student being absent no more than one time. This means we need to consider the probabilities of a student being absent 0 times and 1 time.
Step 2: Calculate the Probability of Being Absent 0 Times
The probability of a student being absent 0 times is given as 0.2.
Step 3: Calculate the Probability of Being Absent 1 Time
The probability of a student being absent 1 time is given as 0.5.
Step 4: Calculate the Total Probability of Being Absent No More Than 1 Time
To find the total probability of a student being absent no more than 1 time, we need to add the probabilities of being absent 0 times and 1 time.
Total Probability = Probability of being absent 0 times + Probability of being absent 1 time Total Probability = 0.2 + 0.5 Total Probability = 0.7
Conclusion
Therefore, the probability in any given week that a randomly selected student will be absent no more than one time is 0.7 or 70%.
Frequently Asked Questions (FAQs)
Q: What is the probability distribution provided in the problem?
A: The probability distribution provided shows the number of absences and their corresponding probabilities.
Q: What is the probability of a student being absent 0 times?
A: The probability of a student being absent 0 times is 0.2.
Q: What is the probability of a student being absent 1 time?
A: The probability of a student being absent 1 time is 0.5.
Q: How do we calculate the total probability of being absent no more than 1 time?
A: To calculate the total probability of being absent no more than 1 time, we need to add the probabilities of being absent 0 times and 1 time.
Q: What is the total probability of being absent no more than 1 time?
A: The total probability of being absent no more than 1 time is 0.7 or 70%.
Q: What does the probability distribution tell us about the number of absences?
A: The probability distribution tells us about the likelihood of a student being absent a certain number of times.
Q: How can we use the probability distribution to make predictions about student absences?
A: We can use the probability distribution to make predictions about student absences by considering the probabilities of different numbers of absences.
Q: What are some potential applications of the probability distribution in real-world scenarios?
A: The probability distribution can be used in real-world scenarios such as predicting student attendance, planning for staff absences, and making decisions about school policies.
Q: How can we update the probability distribution to reflect changes in student attendance patterns?
A: We can update the probability distribution by collecting new data on student attendance and recalculating the probabilities.
Q: What are some potential limitations of the probability distribution?
A: Some potential limitations of the probability distribution include the assumption of independence between student absences and the potential for biases in the data.
Q: How can we address the limitations of the probability distribution?
A: We can address the limitations of the probability distribution by collecting more data, using more advanced statistical models, and considering potential biases in the data.