Answer:
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Step-by-step explanation:
We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.
The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
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Remember that the area of a circle is π*radius^2
Remember that there are 360<span>° in a circle.
</span>The angle of the unshaded part would be 360° minus the shaded part of 60<span>°.
</span>360°- 60° = 300<span>°
</span>Since the area of a circle is πr^2, and the section of the circle is 300°, or 300/360 = 5/6 or one full circle, the area of the unshaded region is
(5/6)π*radius^2
= (5/6)π*12^2
= 120π units^2
Please comment if you have any questions!
Its 37 feet, subtract 24-13 and when you get your answer, round it to nearest tenth.