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Probability of a Confidence Interval

  1. Jul 31, 2008 #1
    What's the probability that a confidence interval (with alpha=10%), will have at least 85 of 100 predicted means within the calculated interval range (xbar +/- 1.645(sigma/sqrt(n)))?

    I understand that on average 90% of my means will be located in this range (and I know how to find this range), but the figure 90% is an AVERAGE.

    Suppose I do this experiment ONCE, and only once. What's the probability that at least (>=) 85 (of the 100, or 85%) of the mean values will be within this range?

    Assumptions: Normal (by Central Limit Theorem as n=100 is greater than 30)

  2. jcsd
  3. Jul 31, 2008 #2


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    sum(n=85,100,.9^n*.1^(100-n)*binomial(100,n)) ≈ 96% of the time.
  4. Jul 31, 2008 #3
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