The Trapezoidal rule Tn on the interval [0,5) will be exact for
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The confidence interval is
. This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.
To find the confidence interval, we first find the z-score associated with it:
Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
We calculate the margin of error using
This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85
To find the confidence interval, we first find the z-score associated with it:
Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.
We calculate the margin of error using
This means that the confidence interval is
The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85