A number, x, rounded to 2 significant figures is 1300Write down the error interval for x.
1 answer:
Answer:
.
Step-by-step explanation:
It is given that a number, x, rounded to 2 significant figures is 1300.
It is possible if,
1. The value of x is greater than of equal to 1250 and less than or equal to 1300.
i.e., ...(1)
2. The value of x is greater than of equal to 1300 and less than 1350.
i.e., ...(2)
On combining (1) and (2), we get
1350 is not included in the error interval for x.
Interval notation is .
Therefore, the error interval for x is .
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Answer:
The confidence interval on this case is given by:
(1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:
So then the mean for this case is 69.505
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 represent the sample size
Assuming the X follows a normal distribution
The confidence interval on this case is given by:
(1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:
So then the mean for this case is 69.505