Asociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. their mean score is 76.2 and their standard deviation is 21.4. construct the 95% confidence interval for the standard deviation, σ, of the scores of all subjects. a. 17.5 < σ < 27.8b. 17.2 < σ < 27.2c. 285.61 < σ < 858.49d. 16.6 < σ < 28.6e. 16.9 < σ < 29.3

e. 16.9<\sigma<29.3

Step-by-step explanation:

As per given , we have

n= 27 ,  , s=21.4

Critical value using Chi-square table:-

Confidence interval for standard deviation:

Hence, the 95% confidence interval for the standard deviation, σ, of the scores of all subjects :

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240