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.
Answer:
volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.
Step-by-step explanation:
The formula to find volume of sphere is:
Volume of sphere = 4/3 π r^3
if radius is divided by 2 i.e r/2
Volume of sphere if r/2 = 4/3 π (r/2)^3
= 4/3 π r^3/8
= (4/3 π r^3) / 8
= (Volume of sphere 1)/8
So, volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.
36 and 144
Explanation
Two Angles are Supplementary when they add up to 180 degrees
Step 1
Let
x= angle 1
y= angle2
The measure of one angle is four times the measure of the other angle,then
x and y are supplementary angles , then
Step 2
use Equation (1) and (2) to find x and y
replace Equation (1) in Equation (2)
replace the value of y= 36 in equation (1) to find x
Hence, the answer is 36 and 144
3(2x-6) when distributed = 6x - 18
Answer:
Yes
Step-by-step explanation:
7/8 + 5/8 = 12/8 = 1 1/2
