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lana66690 [7]
3 years ago
13

Suppose that a jewelry store tracked the amount of emeralds they sold each week to more accurately estimate how many emeralds to

keep in stock. At the end of one year, the store used the weekly sales information to construct a 95% confidence interval for the mean number of emeralds sold per week. The confidence interval they calculated was ( 2.13 , 3.37 ) . Use the confidence interval to find the point estimate for the mean and the margin of error. Give your answers precise to two decimal places.
Mathematics
1 answer:
RUDIKE [14]3 years ago
5 0

Answer:

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75

And for the margin of error we have the following estimation:

ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62

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".

\bar X represent the sample mean

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75

And for the margin of error we have the following estimation:

ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62

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Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29. Writ
zepelin [54]

Part A)

So we need the graph to pass through these points:

time = 2 and price=$14 -> (2,14)

time= 5 and price = $29 -> (5,29)

Standard form:

Ax+By = C

Let’s replace the points:

A*2+B*14=C

A*5+B*29=C

Let’s eliminate variables:

(A*2+B*14)-(A*5+B*29)=C-C

A*2+B*14-A*5-B*29=0

-3A-15B=0

-3A=15B

A=15B/-3

A=-5B

There are several numbers that verify this proportion. For example, if B=1, A=-5 (you can try others, there is not only 1 correct answer).

So we can make this equation:

-5x+y=C

Then we can calculate C using one point:

-5*2+14=C

-10+14=C

4=C

So one of the possible equations is: -5x+y=4

(Remember there are multiple correct answers for this item)

You can verify it with the other point:

-5*5+29=-25+29=4 ->OK

 

Part B)

Whatever you have found in Part A, you will find the same in Part B when you convert it to function notation. All you have to do is clear y:

-5x+y=4

y=4+5x

So the equation is: f(x)=4+5x


Part C)

First of all, you have to find f(0)

f(x)=4+5x

f(0) =4+5*0=4+0=0

f(0) is ALWAYS the constant not multiplied by x.

So you know it has to cross the y axes in y=4

Now let’s put 0 as y-value:

4+5x=0

5x=0-4=-4

x=-4/5

So now you know it has to cross the x axes in x=-4/5.

So you can put those intersections in the graph and you draw the line through those points. Labels: horizontal axes is x, and in this case represents time; vertical axes is y, and in this case represents price.

Remember there are other methods, too :)

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Hi, I'm so sorry I can't answer that. but I have something you can answer that. Search in browser or anything searcher that you have "Quickmath" or "Cymath" all your equations,problems can solved

Step-by-step explanation:

i hope it helps

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Answer:

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Step-by-step explanation:

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