According to Euclid’s second postulate, how far can the line segment shown be extended in either direction?
2 answers:
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<h2>Answer</h2>
0.43
<h2>Explanation</h2>Remember that
Since the problem is telling us "Among tenth graders", we must focus on the 10th graders row only. From the row, we can infer that the frequency is the number of 10th graders who prefer going to sporting events, so . Now, the sum of all frequencies will be the sum of all the 10th graders, so
. Let's replace the values:
And rounded to the nearest hundredth:
Answer:
The 90% confidence interval would be given by (57.006;62.994)
Step-by-step explanation:
Previous concepts
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".
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".
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=30 represent the sample size
Assuming the X follows a normal distribution
The sample mean is distributed on this way:
The confidence interval on this case is given by:
(1)
The next step would be find the value of ,
,
and
Using the normal standard table, excel or a calculator we see that:
Since we have all the values we can replace:
So on this case the 90% confidence interval would be given by (57.006;62.994)