Find the 90% confidence interval for the population standard deviation given the following.

n = 51, x = 11.49, s = 2.34 and the distribution is normal.

a. 1.92 < σ < 3.25
b. 2.01 < σ < 2.81
c. 1.37 < σ < 1.91
d. 10.28 < σ < 14.32

b. 2.01 < σ < 2.81

Step-by-step explanation:

The 90% confidence interval for the population standard deviation is calculated as:

   < σ <

Where n is equal to 51, s is equal to 2.34, is 10%, is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of in the right tail and is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of in the right tail.

So, replacing n by 51, s by 2.34, by 67.50 and by 34.76, we get that the The 90% confidence interval is equal to:

< σ <

2.01 < σ < 2.81

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

the line of