A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data
1 answer:
Answer:
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
Step-by-step explanation:
The margin of error of a confidence interval is given by:
In which is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.
In this question:
The narrower C.I. is the 95%, and the wider is the 99%. So
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
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Answer:
Step-by-step explanation:
So, we know that the center of the circle is at (-6, -7/6).
To find the equation of our circle that is tangent to the x-axis, we just need to find the vertical distance from our center to the x-axis.
Our center is at (-6, -7/6). The vertical distance from this to the x-axis directly above will be (-6, 0).
So, find our distance by subtracting our x-values:
Subtract:
So, our distance, which is also our radius, will be 7/6.
Now, we can use the standard form for a circle, which is:
Where (h, k) is the center and r is the radius.
Substitute -6 for h, -7/6 for k, and 7/6 for r. This yields:
We can confirm by graphing (using a calculator):
