Probability of a Confidence Interval

[shalomhk]

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)


Thanks!

[CRGreathouse]

sum(n=85,100,.9^n*.1^(100-n)*binomial(100,n)) ≈ 96% of the time.

[shalomhk]

Thanks!