19.use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. assume that the population has a normal distribution. round the confidence interval limits to one more decimal place than is used for the original set of data.
the amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.9, 15.2, 15.3, 15.2, 15.3, 15.8, 15.1, 15.2 find a 98% confidence interval for the population standard deviation
with explain how you get there

0.19 < σ < 0.72

Step-by-step explanation:

The sample standard deviation is 0.30.

The population variation can be estimated between:

(n−1) s² / χ²α/2 < σ² < (n−1) s² / χ²(1−α/2)

At 98% confidence and 7 degrees of freedom, χ²α/2 = 18.5 and χ²(1−α/2) = 1.24.

(8−1) 0.30² / 18.5 < σ² < (8−1) 0.30² / 1.24

0.034 < σ² < 0.512

0.19 < σ < 0.72

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: