Answer:
The circumference of circle is: 31.714 cm
Step-by-step explanation:
Let C be the circumference of the circle
And A be the area of circle
It is given that:
We have to find the radius first so that it can be used to find the circumference
The area of circle is given by the formula:
Putting the value of area
Taking square root on both sides
Now
Putting the value of radius
Hence,
The circumference of circle is: 31.714 cm
Answer:
a)
b)
c)
The 95% confidence interval is given by (13.164.15.136)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Part a
12.6 14.4 14.7 14.5 15.2 13.5.
Assuming that the men in this study are representative of the population of all men, what is an estimate of the population mean increase in height after three full days in bed?
For this case the best estimate for the mean is the average given by this formula:
For our case we are taking differences so would be the mean of differences and we got:
Part b
Assuming 95 % of confidence level. In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.025,5)" for
"=T.INV(1-0.025,5)" for
The critical value
Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
First we calculate the sample deviation for the differences with this formula:
Part c
The interval for the mean is given by this formula:
And calculating the limits we got:
The 95% confidence interval is given by (13.164.15.136)
<em><u>Solution:</u></em>
Given that,
The drawing of a building shown below has a scale of 1 inch to 30 feet
1 inch = 30 feet
The drawing of the building of this problem has the height of 1.25 inches and base of 0.75 inches
<em><u>Thus actual height is given as:</u></em>
height = 1.25 inches
<em><u>The actual base is given as:</u></em>
base = 0.75 inches
Thus actual base is 22.5 feet