a) The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

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

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".

If the distribution for X is normal or if the sample size is large enough we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

Part a

The formula is given by mean $\pm$ the margin of error. Where the margin of error is the product between the critical value from the normal standard distribution at the confidence level selected and the standard deviation for the sample mean.

Part b

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

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

5 0

3 years ago

Amelia wants to paint three walls in her family room two walls are 26 feet long by 9 feet wide the other wall is 18 feet long by

Svetllana [295]

26 by 9
Area = L*W
Area = 26 * 9
Area = 234 square feet but there are 2 such walls
Area = 234 * 2
Area = 468 square feet total for these walls.

18 by 9
Area = L*W
Area = 18 * 9
Area = 162 square feet

Total area = 468 + 162 = 630 square feet.

1 gallon covers 250 square feet
x gallon covers 630 square feet

1/x = 250/630
250 x = 1 * 630
x = 630 / 250
x = 2.52 gallons. It is best that she buy 3 gallons of paint.

7 0

3 years ago

What is the slope-intercept form of the linear equation x + 4y = 12?

Anna11 [10]

4y = 12 - x
y = 3 - 1/4x

4 0

3 years ago