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stich3
3 months ago
12

Fire load (MJ/m2) is the heat energy that could be released per square meter of floor area by combustion of contents and the str

ucture itself. The following cumulative percentages are for fire loads in a sample of 388 rooms:
Fire load (MJ/m2) is the heat energy that could be
Value 0 150 300 450 600 750 900
Cumulative % 0 19.0 37.0 61.9 76.5 86.3 93.0
Value 1050 1200 1350 1500 1650 1800 1950
Cumulative % 95.0 97.8 98.1 99.5 99.6 99.8 100.0
(a) What proportion of fire loads are less than 600? At least 1200? (Round your answers to three decimal places.)
(b) What proportion of the loads are between 600 and 1200? (Round your answer to three decimal places.)
Mathematics
1 answer:
Leona [12.6K]3 months ago
8 0

Answer:

a)

The percentage of fire loads under 600 is 0.765

The percentage of fire loads of at least 1200 is 0.022

b)

The percentage of fire loads in the range of 600 to 1200 is 0.213

Step-by-step explanation:

The cumulative percentages are provided for varying x values.

Value (x)      Cumulative percent

0                   0

150              0.19

300             0.37

450             0.619

600             0.765

750             0.863

900             0.93

1050            0.95

1200            0.978

1350            0.981

1500            0.995

1650           0.996

1800          0.998

1950           1

a)

The percentage of fire loads below 600

P(x<600)=F(600)=0.765

Given the cumulative percentages, the result for 450 illustrates the ratio of fire loads below 600.

The proportion of fire loads of at least 1200

P(X≥1200)=1-F(1200)=1-0.978=0.022

b)

To find the percentage of loads between 600 and 1200

P(600≤X≤1200)=?

P(a≤X≤b)=F(b)-F(a)

P(600≤X≤1200)=F(1200)-F(600)=0.978-0.765=0.213

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