G(x) = x^2 + 55 What is the minimum value of the given function?

The weights of 83 randomly selected windshields were found to have a variance of 1.88. Construct the 95% confidence interval for

Morgarella [4.7K]

Answer:

95% confidence interval for the population variance = (1.42 , 2.62).

Step-by-step explanation:

We are given that the weights of 83 randomly selected windshields were found to have a variance of 1.88.

So, firstly the pivotal quantity for 95% confidence interval for the population variance is given by;

P.Q. = $\frac{(n-1)s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, $s^{2}$ = sample variance = 1.88

$\sigma^{2}$ = population variance

n = sample of windshields = 83

So, 95% confidence interval for population variance, $\sigma^{2}$ is;

P(58.85 < $\chi^{2} __8_2$ < 108.9) = 0.95 {As the table of $\chi^{2}$ at 82 degree of freedom

gives critical values of 58.85 & 108.9}

P(58.85 < $\frac{(n-1)s^{2} }{\sigma^{2} }$ < 108.9) = 0.95

P( $\frac{ 58.85}{(n-1)s^{2} }$ < $\frac{1 }{\sigma^{2} }$ < $\frac{108.9}{(n-1)s^{2} }$ ) = 0.95

P( $\frac{ (n-1)s^{2}}{108.9 }$ < $\sigma^{2}$ < $\frac{ (n-1)s^{2}}{58.85 }$ ) = 0.95

95% confidence interval for $\sigma^{2}$ = ( $\frac{ (n-1)s^{2}}{108.9 }$ , $\frac{ (n-1)s^{2}}{58.85 }$ )

= ( $\frac{ (83-1)\times 1.88}{108.9 }$ , $\frac{ (83-1)\times 1.88}{58.85 }$ )

= (1.42 , 2.62)

Therefore, 95% confidence interval for the population variance of the weights of all windshields in this factory is (1.42 , 2.62).

8 0

3 years ago

What’s the y- intercept and x-intercept of y = 3/4x + 3

DochEvi [55]

Answer:

see below

Step-by-step explanation:

y = 3/4x + 3

To find the y intercept, let x =0 and solve for y

y = 0+3

The y intercept is 3

To find the x intercept, let y =0 and solve for y

0 = 3/4x+3

-3 = 3/4x

-3 *4/3 = 3/4x*4/3

-4 =x

The x intercept is -4

3 0

3 years ago

Read 2 more answers

I need help in this please! thank you so much!

Anna35 [415]

Answer:

C) p(x) has a zero between x=2 and x=4

Step-by-step explanation:

For a polynomial p(x), $p(a)=R$ means that, when p(x) is divided by $x-a$ , the remainder is $R$ .

This is called the remainder theorem

Therefore $p(2)=1$ , $p(4)=-1$ means that when p(x) is divided $x-2$ and $x-4$ is 1 and $-1$ respectively.

Also the Intermediate value theorem says that, if p(a) and p(b) have opposite signs then there is a certain $c$ on $(a,b)$ where $f(c)=0$ i.e there is a zero between $a$ and $b$

Therefore the correct answer is C

5 0

4 years ago

√48a^4 b^5 c^3 d simplify and keep it in radical form

Morgarella [4.7K]

I will assume the square root extends all the way across.

$\sqrt{48a^4b^5c^3}$

$\sqrt{2^4\cdot3\cdot a^4b^5c^3}$

$\sqrt{(2^2)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c}$

$\sqrt{(4)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c}$

$\sqrt{(4\cdot a^2 \cdot b^2 \cdot c)^2\cdot3\cdot b\cdot c}$

$4\cdot a^2\cdot b^2\cdot c\sqrt{3\cdot b\cdot c}$

$\boxed{4a^2b^2c\sqrt{3bc}}$

3 0

4 years ago

A video game is on sale for 30% off the regular price of 50$. What is the sale price of the game?

Readme [11.4K]

It is $15.
You have to do: $15 times .30

6 0

3 years ago

Read 2 more answers

G(x) = x^2 + 55 What is the minimum value of the given function?​

G(x) = x^2 + 55 What is the minimum value of the given function?