SOLUTION: There are 267 students in faculty and each of them spends approximately 5.625 hours daily in the reading room. Reading room works 8 hours a day. How many seats must be in the readi

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Question 1192605: There are 267 students in faculty and each of them spends approximately 5.625 hours daily in the reading room. Reading room works 8 hours a day. How many seats must be in the reading room that the probability of finding a free seat is not less than 0.78?

Answer by CPhill(1959) (Show Source):
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**1. Calculate the maximum number of students potentially in the reading room at any given time:**
* **Total student-hours:** 267 students * 5.625 hours/student = 1503.125 student-hours
* **Maximum concurrent students:** 1503.125 student-hours / 8 library hours = 187.89 students
* **Round up:** 188 students (since we can't have a fraction of a student)
**2. Calculate the number of seats needed to accommodate at least 78% of students:**
* **Seats required:** 188 students / 0.78 = 241.03 students
* **Round up:** 242 seats
**Therefore, the reading room should have at least 242 seats to ensure that at least 78% of students can find a free spot.**
**Note:** This calculation assumes a uniform distribution of student library usage throughout the day. In reality, there may be peak times with higher student traffic, which would require a more robust analysis and potentially more seats.