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Bess [88]
3 years ago
14

Find the 90% confidence interval for the population standard deviation given the following.

Mathematics
1 answer:
lions [1.4K]3 years ago
5 0

Answer:

b. 2.01 < σ < 2.81

Step-by-step explanation:

The 90% confidence interval for the population standard deviation is calculated as:

\sqrt{\frac{(n-1)*s^{2} }{X^2_{\alpha/2 } } }    < σ < \sqrt{\frac{(n-1)*s^{2} }{X^2_{1-\alpha/2 } } }

Where n is equal to 51, s is equal to 2.34, \alpha is 10%, X^{2} _{\alpha /2} is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of \alpha /2 in the right tail and X^{2} _{1-\alpha /2} is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of 1-\alpha /2 in the right tail.

So, replacing n by 51, s by 2.34, X^{2} _{\alpha /2} by 67.50 and X^{2} _{1-\alpha /2} by 34.76, we get that the The 90% confidence interval is equal to:

\sqrt{\frac{(51-1)*2.34^{2} }{67.50} } } < σ <\sqrt{\frac{(51-1)*2.34^{2} }{34.76} } }

2.01 < σ < 2.81

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Elden [556K]

Answer:

The answer is "cirtical\  points \ (x,g(x))\equiv  (e,0),(e+3,\frac{27}{e^3})"

Step-by-step explanation:

Given:

g(x) = (x-e)^3e^{-(x-e)}

Find critical points:

g(x) = (x-e)^3e^{(e-x)}

differentiate the value with respect of x:

\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r}  \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3]

critical points g'(x)=0

\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3

So,

The critical points of (x,g(x))\equiv  (e,0),(e+3,\frac{27}{e^3})

7 0
3 years ago
If f = {(-1, 0), (-2, 2), (-3, 4), (-4, 6), (-5, 8)}, what is the range?
raketka [301]

Answer:

{0, 2, 4, 6, 8 }

Step-by-step explanation:

the range is the y- coordinates of the ordered pairs , then

range { 0, 2, 4, 6, 8 }

5 0
2 years ago
Please help compare these integers by typing the symbol that would make the statement true
faust18 [17]
>
Positive integers are always greater.
3 0
3 years ago
In two or more complete sentences, explain how to solve the cube root equation, <img src="https://tex.z-dn.net/?f=%20%5Csqrt%5B3
nordsb [41]
Isolate the root expression:

\sqrt[3]{x+1}+2=0\implies\sqrt[3]{x+1}=-2

Take the third power of both sides:

\sqrt[3]{x+1}=-2\implies(\sqrt[3]{x+1})^3=(-2)^3

Simplify:

(\sqrt[3]{x+1})^3=(-2)^3\implies x+1=-8

Isolate and solve for x:

x=-9

Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When x=-9, we have

\sqrt[3]{-9+1}=\sqrt[3]{-8}=\sqrt[3]{(-2)^3}=-2

as required.
5 0
3 years ago
A student makes a ​$10.50 purchase at the bookstore with a​ $20 bill. The store has no bills and gives the change in quarters an
Leviafan [203]

Answer: he collected 22 quarters and 8 fifty-cent pieces

Step-by-step explanation:

Given;

The total amount of money he is to collect is;

A = 20 - 10.50 = $9.50

Let x represent the number of quarter he collected.

Then the number of fifty-cent pieces he collected will be; 30-x

Therefore we can represent it with the equation below;

0.25x + 0.50(30-x) = 9.50

0.25x + 15 - 0.50x = 9.50

0.25x = 15-9.50

x = (15-9.50)/0.25

x = 5.50/0.25

x = 22

The number of fifty-cent is equal to;

30-x = 30-22 = 8

Therefore, he collected 22 quarters and 8 fifty-cent pieces

3 0
3 years ago
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