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Juli2301 [7.4K]
3 years ago
11

If the square root of n is approximately equal to 4.2, then n is between _____.

Mathematics
2 answers:
Sliva [168]3 years ago
7 0

Answer:

16 and 25

Step-by-step explanation:

Given that the square root of n = 4.2, let's find an expression for this, then find the possible value of n.

Thus:

\sqrt{n} = 4.2

Solve for n. Square both sides.

(\sqrt{n})^2 = (4.2)^2

n = 17.64

Therefore, if the sqrae root of n was approximately equal to 4.2, then we can conclude that n is between 16 and 25.

kirill [66]3 years ago
6 0

Answer:

a

Step-by-step explanation:

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n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92

So the answer for this case would be n=92 rounded up to the nearest integer

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 for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =1.5 and we are interested in order to find the value of n, if we solve n from equation (b) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 92% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.04;0;1)", and we got z_{\alpha/2}=1.75, replacing into formula (b) we got:

n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92

So the answer for this case would be n=92 rounded up to the nearest integer

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