Two sides of a triangle are 4 cm and 7 cm. What can be the length of its third side to make the triangle possible?
1 answer:
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Answer:
B. 3.414 +/-.00149
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".
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation known
n=3 represent the sample size
Confidence interval
Since the population standard deviation is known, the confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean we can use the following formula:
(2)
The mean calculated for this case is
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a tabel 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 (3.413;3.415) The best option for this case is:
B. 3.414 +/-.00149