Carolyn says that point A and point B represent opposite integers. a. What is the opposite of the integer represent by point A?
By point B? b. Do you agree with Carolyn? Explain
1 answer:
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Answer:
See attached picture to view the graph
Step-by-step explanation:
Start by analyzing how this average idea works:
If only one member goes to the trip, it will cost him/her $1000+$200 = $1200.
If two members go to the trip, then they will share the cost as per the following: ($1000+ $200 + $200 = $1400) which they will be dividing into two people, thus costing each of them $700.
Notice that the general function that represents such average will be given by:
Plot such function in the two dimensional plane, and you will get the asymptotic behavior shown in the attached image.
Answer:
a) The 99% confidence interval would be given by (346.708;453.292)
b) The 99% confidence interval would be given by (338.445;461.555)
Step-by-step explanation:
1) 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".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n=15 represent the sample size
2) Part a
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (346.708;453.292)
3) Part b
For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.
The confidence interval for the mean is given by the following formula:
(1)
We need to find the degrees of freedom first df=n-1=15-1=14
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (338.445;461.555)