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ivann1987 [24]
1 year ago
10

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on con

structing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 98%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 23 years. (Use Excel to find the appropriate critical value and round it to 3 decimal places.)
Mathematics
1 answer:
AlladinOne [14]1 year ago
8 0

Using the z-distribution, a sample size of 180 is needed for the estimate.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

The margin of error is given by:

M = z\frac{\sigma}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • z is the critical value.
  • n is the sample size.
  • \sigma is the standard deviation for the population.

In this problem, we have a 98% confidence level, hence\alpha = 0.98, z is the value of Z that has a p-value of \frac{1+0.98}{2} = 0.99, so the critical value is z = 2.327.

The population standard deviation is of \sigma = 23, and to find the sample size, we have to solve for n when M = 4.

Hence:

M = z\frac{\sigma}{\sqrt{n}}

4 = 2.327\frac{23}{\sqrt{n}}

4\sqrt{n} = 2.327 \times 23

\sqrt{n} = \frac{2.327 \times 23}{4}

(\sqrt{n}) = \left(\frac{2.327 \times 23}{4}\right)^2

n = 179.03.

Rounding up, as a sample size of 179 would result in an error slightly above 4, a sample of 180 is needed.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

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Find the sum of the sequence. 45+46+47+48+...+108
Anna11 [10]
We know, S = n/2 [ a + l ]
Here, a = 45
l = 108

Calculation of n:
a(n) = a + (n - 1)d
108 = 45 + (n - 1)1
108 - 45 = n - 1
63 + 1 = n
n = 64

Now, substitute in the expression:
S = 64/2 [ 45 + 108 ]
S = 32 [ 153 ]
S = 4896

In short, Your Answer would be 4896

Hope this helps!
7 0
3 years ago
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Riley has set up a six week payment schedule to pay for his upcoming school camp. he has already put down a 15 percent deposit a
anyanavicka [17]

Answer:

$32.30 each week

Step-by-step explanation:

Deposit = 15%  = $34.20

⇒ total cost of camp = (34.20 ÷ 15) x 100 = $228

Balance left after deposit = 228 - 34.20 = $193.80

If paying the remaining balance in 6 weekly installments,

⇒ weekly payment = 193.80 ÷ 6 = $32.30

4 0
2 years ago
Write 5 5/8 as a improper fraction<br> A. 33/8<br> B. 45/8<br> C. 40/8<br> D. 35/8
Vikentia [17]

Answer:

I believe this would be B

Step-by-step explanation:

The way I do improper fractions is called the 'boot'

It is where you take the whole number and the denominator and circle both of them so it kind of looks like a boot and you multiply those together.

So 5 * 8= 40 then you add your numerator to that which gets you 45, and you keep the denominator the same

So you end up with 45/8

Sorry if its a little confusing

Hope this helps :)

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2 years ago
A circle has the equation 2x²+12x+2y²−16y−150=0.
KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

(x-h)^{2} +(y-k)^{2}=r^{2} (1)

Where (h,k) are the coordinates of the center and r is the radius.

Now, we are given the equation of this circle as follows:

2x^{2}+12x+2y^{2}-16y-150=0 (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

2(x^{2}+6x+y^{2}-8y-75)=0 (3)

Rearranging the equation:

x^{2}+6x+y^{2}-8y=75 (4)

(x^{2}+6x)+(y^{2}-8y)=75 (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of (a\pm b)^{2}=a^{2}\pm+2ab+b^{2}:

<u>For the first parenthesis:</u>

x^{2}+6x+b^{2}

We can rewrite this as:

x^{2}+2(3)x+b^{2}

Hence in this case b=3 and b^{2}=9:

x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}

<u>For the second parenthesis:</u>

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We can rewrite this as:

y^{2}-2(4)y+b^{2}

Hence in this case b=-3 and b^{2}=9:

y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}

Then, equation (5) is rewritten as follows:

(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16 (6)

<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>

Rearranging:

(x-3)^{2}+(y-4)^{2}=100 (7)

At this point we have the circle equation in the center radius form (x-h)^{2} +(y-k)^{2}=r^{2}

Hence:

h=-3

k=4

r=\sqrt{100}=10

8 0
3 years ago
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