Step-by-step explanation:
So sqrt(40) lies between 6 and 7.
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The confidence interval would be (10.44, 12.16). This means that if we take repeated samples, the true mean lies in 90% of these intervals.
To find the confidence interval, we use:
We first find the z-value associated with this. To do this:
Convert 90% to a decimal: 90% = 90/100 = 0.9
Subtract from 1: 1-0.9 = 0.1
Divide by 2: 0.1/2 = 0.05
Subtract from 1: 1-0.05 = 0.95
Using a z-table (http://www.z-table.com) we see that this is directly between two z-scores, 1.64 and 1.65; we will use 1.645:
To find the confidence interval, we use:
We first find the z-value associated with this. To do this:
Convert 90% to a decimal: 90% = 90/100 = 0.9
Subtract from 1: 1-0.9 = 0.1
Divide by 2: 0.1/2 = 0.05
Subtract from 1: 1-0.05 = 0.95
Using a z-table (http://www.z-table.com) we see that this is directly between two z-scores, 1.64 and 1.65; we will use 1.645: