Rose purchased 2 packs of red pens, 4 packs of black pens, and 3 packs of blue pens. The cost of each pack of pens was $2.50. Th
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Answer:
The margin of error of u is of 3.8.
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 28 - 1 = 27
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.7707
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error of u is of 3.8.
The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes
The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes
The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.
Supposse that the distance from the point to the point
is equal to the distance from
to the point
. Then, by the formula of the distnace we must have
cancel the square root and the 's, and then expand the parenthesis to obtain
then, simplifying we obtain
therfore we must have
this means that the points satisfying the propertie must have first component equal to 5. So we can give a lot of examples of such points: . The set of this points give us a straight line and the points (3,0) and (7,0) are symmetric with respect to this line.