# A certain hotel has 80 rooms. Based on many previous years' occupancy rates

A certain hotel has 80 rooms. Based on many previous years' occupancy rates, the owners of the hotel constructed the table below showing the daily occupancy rates and their probabilities of occurring for the coming summer season. Based on the probability distribution in the table, to the nearest whole number, what is the expected number of rooms that will be occupied on any day during the coming summer season?

- 20
- 25
- 58
- 60
- 75

### Answer

**The correct answer is C. **

The expected occupancy rate is the sum of the products of each occupancy rate and its corresponding probability.

= 0.6(0.2) + 0.7(0.4) + 0.8(0.3) + 0.9(0.1)

= 0.12 + 0.28 + 0.24 + 0.9

= 0.73

To calculate the expected number of rooms that will be occupied during the coming summer season, multiply the expected occupancy rate by the total number of rooms.

= 0.73(80)

= 58 (approximately)