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Lerok [7]
2 years ago
11

You are interested in estimating the the mean weight of the local adult population of female white-tailed deer (doe). From past

data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 19 pounds. What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 98% confidence level, to within 7 pounds of the actual weight?
Mathematics
1 answer:
alisha [4.7K]2 years ago
6 0

Answer:

n=(\frac{2.33(19)}{7})^2 =39.996 \approx 40

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

\sigma=19 represent the assumed population standard deviation

n represent the sample size (variable of interest)  

Confidence =0.98 or 98%

Me=0.07 represent the margin of error for this case

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}  (1)  

And on this case we have that ME =7 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (2)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.01,0,1)", and we got z_{\alpha/2}=2.33, replacing into formula (2) we got:

n=(\frac{2.33(19)}{7})^2 =39.996 \approx 40

So the answer for this case would be n=40 rounded up to the nearest integer

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Step-by-step explanation:

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2 years ago
Jonathan ran five days a week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance jonathan co
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Answer: x\leq17.5


Step-by-step explanation:

Given: The number of days Jonathan ran =  5

The most he ran in 1 day = 3.5 miles

Therefore, the maximum distance he ran in a week= 5\times3.5=17.5\ miles

Let x be the distance  Jonathan could have rum in a week, such that

x\leq17.5

Hence, the required inequality is x\leq17.5.


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3 years ago
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Matthew made slightly larger blanket that was 8 Ft long. Its area is 64 sq ft what is its perimeter?
Andreas93 [3]

Answer:

32 ft

Step-by-step explanation:

Given data

Length= 8ft

Area= 64 f^2

Let us find the width

Area= Length*Width

64= 8* Width

Width= 64/8

Width= 8ft

Hence the perimeter= 2L+2W

P= 2*8+2*8

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5 0
2 years ago
Pleas help me find the answer and show the work to this question
lions [1.4K]

Answer:

Leg\ 1 = 8

Leg\ 2 = 15

Step-by-step explanation:

Given: See Attachment

Required

Determine the length of the legs

To do this, we apply Pythagoras theorem.

Hyp^2 = Adj^2 + Opp^2

In this case:

17^2 = x^2 + (2x- 1)^2

Open Bracket

17^2 = x^2 + 4x^2- 2x-2x + 1

17^2 = 5x^2 - 4x + 1

289= 5x^2 - 4x + 1

Collect Like Terms

5x^2 - 4x + 1 - 289 = 0

5x^2 - 4x - 288 = 0

Solving using quadratic formula:

x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}

So:

x = 8 or x = -7.2

Since, x can't be negative, then:

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One of the leg is:

Leg\ 1 = x

Leg\ 1 = 8

Leg\ 2 = 2x - 1

Leg\ 2 = 2*8 - 1

Leg\ 2 = 16 - 1

Leg\ 2 = 15

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borishaifa [10]

Answer:

432 in.^2

Step-by-step explanation:

The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.

We use the Pythagorean theorem,

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b = sqrt(324 in^2)

b = 18 in

area of rectangle = length * width

A = 24 in. * 18 in.

A = 432 in.^2

6 0
3 years ago
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