To determine

a)

To estimate:

The number of people who died of SARS in Singapore

Answer

For left end points, 24 people

For right end points, 28 people

Explanation

1) Concept:

Area under the graph is

A=limn→∞∑i=1nfxi∆x

where,

∆x=b-an & xi=a+i∆x

2) Calculation:

Here,

∆x=14 days

So using left end points of each interval to estimate the total deaths in given time period,

L6=∑i=16fxi∆x

=140.0079+0.0638+0.1944+0.4435+0.5620+0.4630

=24.2844

 So, the total deaths are 24.

Now use right end points of each interval to estimate the total deaths in given time period.

R6=∑i=16fxi∆x

=140.0638+0.1944+0.4435+0.5620+0.4630+0.2897

=28.2296

So the total deaths are 28.

Conclusion:

For left end points, the total deaths are 24 people in the given time period.

And for right end points, the total deaths are 28 people in the given time period.

To determine

b)

To describe:

How to interpret the number of deaths as an area under a curve

Answer

The number of SARS deaths is approximately equal to the area under the curve for the given interval.

Explanation

Let x be the number of days since March 1, 2003 and f(x) be the number of deaths per day on day x.

So y=f(x) is a continuous function over the given interval [0, 84].

Then the number of SARS deaths is approximately equal to the area under the curve y=f(x) from x=a to x=b.

Conclusion: