Underlying distribution is Normal distribution or Approximate Normal Distribution.
The no of SUVs follow A Binomial distribution with parameters n and p or theta.
Binomial can be approximated by Normal distribution, when n is large and np and nq are > 5
here n =500 quite large
500*0.136 = 5*13.6 =68 > 5
500 * 0.864 = 5*86.4 = 432 >5
Hence we can use Normal distribution for constructing confidence interval.
What we construct is a random interval. We can say that the random interval covers the true value theta with probability 0.95. We cannot say that the probability that theta lies in this interval is 0.95 ( it must be noted that either it will lie or will not lie). If we repeatedly construct te confidence intervals, 95 out of 100 intervals will include the true value of theta.
Dec 17th, 2014
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