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2 answers:
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Answer:
Step-by-step explanation:
Given
Required
Determine the type of roots
Represent Discriminant with D; such that
D is calculated as thus
And it has the following sequence of results
When then the roots of the quadratic equation are real but not equal
When then the roots of the quadratic equation are real and equal
When then the roots of the quadratic equation are complex or imaginary
Given that ; This means that
and base on the above analysis, we can conclude that the roots of the quadratic equation are complex or imaginary
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.