Statistics (Mutual Exclusivity)

[river trench]

Calls that last at least 2 minutes, and no more than 8 minutes,

represent 20 + 42 + 28 = 90 per cent of all calls.

This is because there is no overlap in length (and thus double

counting) of these calls.

i.e if $L$ is the length of the call, then:

$\bullet \quad L \in \big[2,,4\big)$ minutes covers 20 per cent of calls.

$\bullet \quad L \in \big[4,,6\big)$ minutes covers 42 per cent of calls.

$\bullet \quad L \in \big[6,,8\big)$ minutes covers 28 per cent of calls.

$\bullet \quad \text{Hence, }L \in \big[2,,8\big)$ minutes covers $20 + 42 + 28 = 90$ per cent of calls.

Does this make sense?

[frail geyser]

Jay

[random yarrow]

Yes this makes sense, I can see the same logic applies to get 72%. However what I'm asking is how is the equation to what the question is asking the difference between 90 and 72?

[river trench]

The 90% is (2 to 3 minutes) or (3 to 4 minutes) or (4 to 5) or (5 to 6) or (6 to 7) or (7 to 8).

The 72% is (3 to 4 minutes) or (4 to 5 minutes) or (5 to 6) or (6 to 7).

The difference leaves behind only the (2 to 3 minutes) or the (7 to8 minutes), which is what the question sought.