Question

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 0 150 300 450 600 750 Cumulative % 0 35 55 75 95 100 What proportion of fire loads are less than 300? What proportion of fire loads are at least 450? What proportion of fire loads are exactly 750? What proportion of the fire loads are less than 300? What proportion of the fire loads are at least 450?

Answer 1

Answer with explanation:

Given : 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               0 150  300    450   600  750

Cumulative %  0  35   55      75     95  100

Let p represents the proportion of fire loads.

(a) From the above table, the percentage of fire loads less than 300 is 55%,i.e.  proportion=0.55.

Now, the proportion of fire loads are less than 300 will be :-

$P(p<300)= 0.55$

Hence, the proportion of fire loads are less than 300 =0.55

(b) Also, the percentage of fire loads less than 450 is 75%,i.e.  proportion=0.75.

Then, the proportion of fire loads are at least 450 :_

$P(p\geq450)= 1-P(p<450)=1-0.75=0.25$

Hence, the proportion of fire loads are at least 450 =0.25

(c) The percentage of fire loads less than 750 is 100%,i.e. proportion= 1.00.

Then, the proportion of fire loads are exactly 750 :-

$P(p=750)= 1-P(p<750)=1-1=0$

Hence, the proportion of fire loads are exactly 750=0