Solve each equation by using square roots 3x^2-15=0

If 8 is added to twice a number and this sum is multiplied by 3ˏ the result is the number multiplied by 3 and 9 is added to the

9966 [12]

$n-a\ number\\\\(8+2n)\cdot3=3n+9\\\\8\cdot3+2n\cdot3=3n+9\\\\24+6n=3n+9\ \ \ \ /-24\\\\24-24+6n=3n+9-24\\\\6n=3n-15\ \ \ \ /-3n\\\\6n-3n=3n-3n-15\\\\3n=-15\ \ \ \ /:3\\\\3n:3=-15:3\\\\n=-5$

8 0

3 years ago

If Upper X overbar equals 62, Upper S equals 8, and n equals 36, and assuming that the population is normally distributed, c

marishachu [46]

Answer:

The 99% confidence interval would be given by (58.373;65.627)

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

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".

$\bar X=62$ represent the sample mean

$\mu$ population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size

Part a: Confidence interval

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ 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: "=-T.INV(0.005,35)".And we see that $t_{\alpha/2}=2.72$