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3 years ago

How to solve the problem step by step

Mathematics

2 answers:

vlada-n [284]3 years ago

5 0

$5-2+12\div4=3+3=6$

Alex777 [14]3 years ago

3 0

The answer to the expression is 6.

Using pemdas, you can first start to solve this by solving the 12÷4. 12÷4 is equal to 3, so the expression simplifies to:

5-2+3

Then you can add and subtract from left to right.

5-2+3

3+3

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$8.2-2.58\frac{2.2}{\sqrt{18}}=6.86$

$8.2+2.58\frac{2.2}{\sqrt{18}}=9.54$

So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:

$ME= 2.58\frac{2.2}{\sqrt{18}} =1.338$

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".

$\bar X=8.2$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=2.2$ represent the population standard deviation

n represent the sample size

Solution to the problem

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

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

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

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

$8.2-2.58\frac{2.2}{\sqrt{18}}=6.86$

$8.2+2.58\frac{2.2}{\sqrt{18}}=9.54$

So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:

$ME= 2.58\frac{2.2}{\sqrt{18}} =1.338$

8 0

3 years ago

Read 2 more answers