Consider a normal population distribution with the value sigma known. (a) What i

Question

Consider a normal population distribution with the value sigma known. (a) What is the confidence level for the interval x plusminus 2.88 sigma Squareroot n ? % (b) What It the confidence level for the Interval x plusminus 1.48 sigma Squareroot n? % (c) What value of CI formula below results In a confidence level of 99.7%? (x-z_pi 2, sigma/Squareroot n, x+z pi/2, sigma/Squareroot n) z_sigma/2 = (d) Answer the question posed In part (c) for a confidence level of 78% z_sigma/2 = You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

1-/2 =0.9880                          (from the Z value table )

= 0.024

confidence level =1-

                        =1-0.024

                        =0.976

                        =97.6%

1-/2 =0.6844              (from the Z value table )

= 0.6312

confidence level =1-

                        =1-0.6312

                        =0.3688

                        =36.88%

c)confidence level 99.7%

                        = 1-0.997 =0.003

probability P= 1-/2 =1-0.003/2 =0.9985

critical value Z /2(0.9985) =2.96

c) confidence interval =78%

                        = 1- 0.78 =0.22

probability P = 1-/2 =1-0.78/2 =0.61

critical value Z /2(0.61) =0.28

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