There are 12 girls and 13 boysin a classroom how many ways can i select a girl or boy<br>

You start a search for a buried object by marking the center of a field as (0, 0), with coordinates giving distances in yards. C

pychu [463]

The coordinates to the second spot can be represented by the coordinates

(-12 + 3, 8 -11)

Since we are going 3 yards to the east we would be affecting the x-axis and since we are going east we will need to add 3 yards the x axis of the first spot

11 yards south would be affecting the y- axis negatively. We would need to subtract 11 from the y- axis of the first spot.

the coordinates of the second spot would be

-12 +3 = -9

8 -11 = -3

(-9, -3)

7 0

3 years ago

In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

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

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

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

3 years ago

Katie and jennifer are playing a game. katie and jennifer each started with 100 points. at the end of each turn katies points do

ella [17]

It is the fourth round and this is because in round one Katie has 200 and Jenny will have 300.In round two katie will have 400 and Jennifer will have 500.In round 3 Katie will have 600 and and jennifer will have 800.I

3 0

3 years ago

As an estimation we are told £3 is €4.<br> Convert €52 to pounds.

kati45 [8]

Answer:

£69.33

Step-by-step explanation:

4/3=1.33333333333 so that 52*1.33333333333 would convert 52 euros into 52 pounds

7 0

4 years ago

Find slope of (2,2) and (4,b)

elena-14-01-66 [18.8K]

Answer: Use the slope formula to find the slope

m = −2−b/2

4 0

3 years ago

There are 12 girls and 13 boysin a classroom how many ways can i select a girl or boy​

There are 12 girls and 13 boysin a classroom how many ways can i select a girl or boy