Please Give me full answer with all details step by step (8 points; 8 minutes) 5

Question

Please Give me full answer with all details step by step

(8 points; 8 minutes) 5. A random sample of Americans was asked if they think Iran would destroy Israel if Iran acquired nuclewar weapons. In the survey, 298 said "YES" and 44 said "NO". Use the survey results to make an 86% confidence interval for the percent or proportion of all Americans that would answer "YES" to this question. What is the probability that the true percent or proportion of Americans that would answer "YES" next year wl be in next year's confidence interval if you do another survey nlyze next year's data in the same way? Probability

Explanation / Answer

Normal approximation to the binomial calculation:

Standard error of the mean = SEM = x(N-x)/N3 = 0.018

= (1-CL)/2 = 0.070

Standard normal deviate for = Z = 1.476

Proportion of positive results = P = x/N = 0.871

Lower bound = P - (Z*SEM) = 0.845

Upper bound = P + (Z*SEM) = 0.898

b)Probability that true proprtion will be in this confidence interval is 86%

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