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1 year ago

The weekly salaries of a sample of employees at the local bank are given in the table below. Employee Weekly Salary

Mathematics

2 answers:

neonofarm [45]1 year ago

8 0

Answer:

17507.5

Step-by-step explanation:

Given :

Weekly Salary

Anja $245

Raz $300

Natalie $325

Mic $465

Paul $100

Formula given :

$S^2 =\frac{(x_1-\bar x)^2+(x_2-\bar x)^2+....+(x_n-\bar x)^2}{n-1}$

Where $\bar x$ is mean

n = no. of observations

To find: What is the variance for the data?

Solution:

Now to find mean :

$Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}$

$Mean = \frac{245+300+325+465+100}{5}$

$Mean = \frac{1435}{5}$

$Mean = 287$

So, $\bar x = 287$

$x_1 = 245$

$x_2 = 300$

$x_3 = 325$

$x_4 = 465$

$x_5 = 100$

n = 5

Substitute the values in the formula :

$S^2 =\frac{(245-287)^2+(300-287)^2+(325-287)^2+(465-287)^2+(100-287)^2}{5-1}$

$S^2 =\frac{70030}{4}$

$S^2 =17507.5$

Hence the variance of the data is 17507.5

Pachacha [2.7K]1 year ago

5 0

I just took the test and the correct answer is 17,507.5

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Solve: 3.6 (5x4) divided 3+5.0=

zavuch27 [327]

The value of the expression will be 9.

Explanation

Given expression is : $\frac{3.6(5*4)}{3+5.0}$

First we will simplify both numerator and denominator separately using order of operations. So....

$3.6(5*4)=3.6(20)=72\\\\ and\\\\ 3+5.0=8$

Thus the expression....

$\frac{3.6(5*4)}{3+5.0}=\frac{72}{8}=9$

7 0

1 year ago

Students collected data about the capacities of their lungs by inflating balloons with a single breath. they measured the circum

marishachu [46]

The given data is the following:

Student Trial 1 Trial 2 Trial 3 Average
----------- -------- -------- -------- ------------
1 66.0 66.5 68.5 67.0
2 67.5 64.0 70.5 67.3
3 60.3 60.5 60.5 61.0
4 55.0 58.0 59.0 57.3

Let us check the reported averages.
Student 1:
Average = (66.0 + 66.5 + 68.5)/3 = 67.0 Correct
Student 2:
Average = (67.5 + 64.0 + 70.5)/3 = 67.3 Correct
Student 3:
Average = (60.3 + 60.5 + 60.5)/3 = 604 Incorrect
Student 4:
Average = (55.0 + 58.0 + 59.0)/3 = 57.3 Correct

Answer: Student 3

6 0

1 year ago

Read 2 more answers

A snake tank measures 1.8 m x 0.5 m x 0.5 m. What is the surface area of the tank including the top? Use the formula: SA = 2hl+2

olganol [36]

Answer:

4.1

Step-by-step explanation:

1.8 x 0.5 = 0.9

0.5 x 0.5 = 0.25

2(0.9 + 0.9 + 0.25) = 2(1.8 + 0.25) = 2(2.05)

2 x 2.05 = 4.1

Therefore the answer is 4.1

I hope that was helpful!

8 0

1 year ago

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

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".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: