Need help with the following: Consider a normal population distribution with the

Question

Need help with the following:

Consider a normal population distribution with the value of ? known. What is the confidence level for the interval x ± 1.41?/n?

Answer the question posed in part (c) for a confidence level of 78%.

Consider a normal population distribution with the value of ? known (a what is the confidence level for the interval x 99.5 2.81a/vn? Round your answer to one decin a pace. (b) What is the confidence level for the interval X +1.410/Vn? (Round your answer to one decimal place.) 84.5 (c) what value of Za/2 in the CI formula below results in a confidence level of 99.7%? (Round your answer to two decimal places.) a/2 2.97 (d) Answer the question posed in part (c) for a confidence level of 78%. (Round your answer to two decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

b) From standard normal tables, we get:

P( Z < 1.41 ) = 0.9207

Therefore, P(Z > 1.41 ) = 1 - 0.9207 = 0.0793

Therefore due to symmetry,

P( Z < -1.41 ) = 0.0793

Therefore, P( -1.41 < Z < 1.41 ) = 1 - 2*0.0793 = 0.8414

Therefore 84.1% should be the required confidence interval here.

(d) For 78% confidence interval, we have to find K such that:

P( -K < Z < K ) = 0.78

Therefore P(Z < K) = 0.78 + (1 - 0.78)/2 = 0.89

From standard normal tables, we get: P(Z < 1.227 ) = 0.89

Therefore required value here is 1.23

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.