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Fire load (MJ/m²) is the heat energy that could be released per square meter of floor area by combustion of contents and the structure itself. The following cumulative percentages are for fire loads in a sample of 388 rooms:

| Value (MJ/m²) | Cumulative % |
|---------------|--------------|
| 0 | 0 |
| 150 | 19.1 |
| 300 | 37.6 |
| 450 | 62.4 |
| 600 | 77.0 |
| 750 | 86.5 |
| 900 | 93.0 |
| 1050 | 94.8 |
| 1200 | 97.8 |
| 1350 | 98.1 |
| 1500 | 99.5 |
| 1650 | 99.6 |
| 1800 | 99.8 |
| 1950 | 100.0 |

(a) Construct a relative frequency histogram.

Comment on interesting features. (Select all that apply.)

- The typical middle value is somewhere between 150 and 300.
- The typical middle value is somewhere between 300 and 450.
- The relative frequency distribution exhibits a large negative skew.
- The relative frequency distribution is symmetric.
- The relative frequency distribution exhibits a large positive skew.

(b) What proportion of fire loads are less than 600?

Answer :

Final answer:

To construct a relative frequency histogram for fire load data, divide the data into class intervals and calculate the relative frequency. The typical middle value is between 300 and 450, and the distribution exhibits a positive skew. Approximately 62.4% of fire loads are less than 600.

Explanation:

To construct a relative frequency histogram for the given fire load data, we first need to determine the class intervals. From the cumulative percentages provided, we can divide the data into the following classes: 0-150, 150-300, 300-450, 450-600, 600-750, 750-900, 900-1050, 1050-1200, 1200-1350, 1350-1500, 1500-1650, 1650-1800, and 1800-1950. Then, we calculate the relative frequency for each class by dividing the cumulative percentage by 100. Finally, we plot a histogram with the class intervals on the x-axis and the relative frequencies on the y-axis.

(a) From the constructed relative frequency histogram, we can observe that the typical middle value is somewhere between 300 and 450. The relative frequency distribution exhibits a large positive skew.

(b) To determine the proportion of fire loads less than 600, we sum up the relative frequencies for the classes up to 600. Adding the relative frequencies for the classes 0-150, 150-300, and 300-450 gives us the proportion of fire loads less than 600, which is approximately 0.624 or 62.4%.

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