Will a 9m long planks fit into a square room of side 7m? please I really needed help with this one

Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in

seraphim [82]

Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

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: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

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

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

3 0

1 year ago

Roberto's toy car travels at 30 centimeters per second (cm/sec) at high speed and 20 cm/sec at low speed. If the car travels for

igomit [66]

Answer:

1200 cm

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

NEED HELP ASAP!!

juin [17]

The answer is C.

Note when Soro divides both sides by -2.5 to solve the equation. When multiplying/dividing by a negative number, one should always reverse the inequality sign, but Soro forgot to do this.

-2.5x≥-30

After this step, the answer SHOULD HAVE been:

x≤12

Let me know if you need any clarifications, thanks!

8 0

1 year ago

Read 2 more answers

Orthographic projection and isometric projection are two ways to show three-dimensional objects in a two-dimensional space, such

DerKrebs [107]

Answer:

Orthographic Projection is used for making the projects but Isometric Projection is used to have better understanding of the object.

Orthographic drawings are typically two dimensional views of an object. For instance, if you were designing a table, you would draw a top view, side view and a bottom view. Should these three views not fully explain the design of the table other views would need to be drawn. When drawing an perspective view in an orthographic manner, you would utilize a 45 degree triangle for the lines that extend back or forward from the vertical lines. This type of perspective is not a true perspective because you can measure the true length of all the details shown. An isometric drawing is meant to depict a 3D image of an object in what appears to be a perspective view. However, similar to an orthographic perspective, all of the lines in an isometric drawing can be measured to their true length. What makes it different from an orthographic perspective is that its angled lines are drawn at 30 or 60 degrees or divisions of them. Drawing this by hand you would use a 30/60/90 triangle.

In either case, both types of perspectives can be accurately measured with a ruler in order to know the objects measurements.

Step-by-step explanation:

5 0

1 year ago

Use an inequality symbol (<, >, =, ≥) to compare −17 ____ −1

o-na [289]

A is the right answer

God Bless

5 0

2 years ago