Tìm cực trị của hàm số <br> z=x^{4} - 8x^{3} + 16x^{2} + y^{2}

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below.

garik1379 [7]

Answer:

The 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

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".

$\bar X_1 =9.2$ represent the sample mean 1

$\bar X_2 =8.8$ represent the sample mean 2

n1=27 represent the sample 1 size

n2=30 represent the sample 2 size

$\sigma_1 =0.3$ population standard deviation for sample 1

$\sigma_2 =0.1$ population standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Solution to the problem

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =9.2-8.8=0.4$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$0.4-1.96\sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}=0.281$

$0.4+1.96\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=0.519$

So on this case the 95% confidence interval would be given by $0.281 \leq \mu_1 -\mu_2 \leq 0.529$

6 0

4 years ago

1. Zoey took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.20 plus $3.25 per mile. The tota

RoseWind [281]

equation:3.25x+1.2=40.2

ansrew:x=12

5 0

3 years ago

Help please. I attempted, but I couldn't succeed.

german

Answer:

y=(3/2)x+-14

First blank: 3

Second blank:2

Last blank:-14

Step-by-step explanation:

The line form being requested is slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Also perpendicular lines have opposite reciprocal slopes so the slope of the line we are looking for is the opposite reciprocal of -2/3 which is 3/2.

So the equation so far is

y=(3/2)x+b.

We know this line goes through (x,y)=(4,-8).

So we can use this point along with our equation to find b.

-8=(3/2)4+b

-8=6+b

-14=b

The line is y=(3/2)x-14.

3 0

3 years ago

What is 3 3/4×2 4/5 in simplest form

Archy [21]

Answer:

10.5 = 10 1/2

Step by step:

(3 3/4)(2 4/5)

= 15/4(2 4/5)

=15/4(14/5)

=21/2

=10 1/2

4 0

3 years ago

PLSS HELP ME WITH THIS! 15 POINTS!

irina [24]

Answer:

2w - 13

Step-by-step explanation:

here we just simplify the expression,

3w - 4 - w - 9

becomes:

2w - 13

5 0

2 years ago

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Tìm cực trị của hàm số z=x^{4} - 8x^{3} + 16x^{2} + y^{2} - 2y +1