−2.5x+8=24, what is x

1 answer:

8 0

X = -6.4

First, you would subtract 8 on both sides:

-2.5x + 8 - 8 = 24 - 8

The 8 cancels out on the left side of the equation, and 24 - 8 = 16

Next, divide both sides by -2.5, to get rid of the number that is multiplying by x.

-2.5x/-2.5 = 16/-2.5
= x = -6.4

*Remeber, when dividing a negative by a positive, the answer is negative. In this case, 6.4 is negative.

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$n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38$

So then the minimum sample to ensure the condition given is n= 38

Step-by-step explanation:

Notation

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

$\mu$ population mean (variable of interest)

$\sigma=12$ represent the population standard deviation

n represent the sample size

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean 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 =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is $\alpha=1-0.96 =0.04$ . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got $z_{\alpha/2}=2.054$ , replacing into formula (b) we got: