We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

$\begin{gathered} 1-\alpha=0.98 \\ \alpha=0.02 \end{gathered}$

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

$CI(\mu)=\lbrack x-Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}},x+Z_{1-\frac{\alpha}{2}}\cdot\frac{\sigma}{\sqrt[]{n}}\rbrack$

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

$CI(\mu)=\lbrack30.0-Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}},30.0+Z_{0.99}\cdot\frac{2.40}{\sqrt[]{28}}\rbrack$

Where (from tables):

$Z_{0.99}=2.33$

Finally, the interval at 98% confidence level is:

$CI(\mu)=\lbrack28.94,31.06\rbrack$

4 0

1 year ago

What quadrant would you find the ordered pair ( correct answer gets brainliest)

zhenek [66]

Answer:All coordinate pairs that are in Quadrant I will have a positive x value and a positive y value. All coordinate pairs that are in Quadrant II will have a negative x value and a positive y value. All coordinate pairs that are in Quadrant III will have a negative x value and a negative y value.

Step-by-step explanation:ebob

8 0

3 years ago

In the figure below, AB=AE, AC=AD and AP is perpendicular to BE. Prove that BC=DE.

NISA [10]

Step-by-step explanation:

1) In the figure, as AB is equal to AE, ABE is an equilateral triangle.

As AP is perpendicular to BE

=> AP is the height of the triangle ABE.

In an equilateral triangle, the median and the height is the same, so that AP is also the median of the triangle.

=> P is the midpoint of BE

=> PE = PB

2) In the figure, as AC = AD, so that ACD is an equilateral triangle.

As AP is perpendicular to BE, so that it is perpendicular to CD as well

=> AP is the height of the triangle ACD

In an equilateral triangle, the median and the height is the same, so that AP is also the median of the triangle ACD.

=> P is the midpoint of CD

=> PC = PD

We have:

+) PB = PE

+) PC = PD

=> PB - PC = PE - PD => BC = DE

5 0

4 years ago

A golden rectangle has side lengths in the ratio of about 1: 1.618 if the long side of a golden rectangle is 35 cm what is its a

lakkis [162]

Answer:

The answer to your question is 757.1 cm²

Step-by-step explanation:

Data

Ratio 1: 1.618

long side = 35 cm

Area = ?

Process

1.- Use proportions to solve this problem

1 : 1.618 :: x : 35

x = (35 x 1) / 1.618

x = 35 / 1.618

x = 21.63

2.- Calculate the area of the rectangle

Area = base x height

Area = 35 x 21.63

Area = 757.1 cm²

5 0

4 years ago