Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 18 feet. The perimeter of the dog run mu
1 answer:
Answer:
Step-by-step explanation:
Given, the length of the rectangular dog run is 18 feet.
Formula: Perimeter = 2 ( length + width)
Let width be x.
Then, Perimeter = 2 (18 + x ) feet
The perimeter of the dog run must be at least 42 feet and no more than 72 feet.
That is
Divide inequality by 2, we get
Subtract 18 from each side, we get
Required inequality :
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Answer:
The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:
n=28
Step-by-step explanation:
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".
Assuming the X follows a normal distribution
And the distribution for is:
We know that the margin of error for a confidence interval 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:
If we solve for n from formula (1) we got:
And we have everything to replace into the formula:
And this value agrees with the sample size given.
For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:
And now we can replace the new value of Me and see what we got, like this:
And if we round up the answer we see that the value of n to ensure the margin of error required $ is n=28.