# Probability of a Confidence Interval

1. Jul 31, 2008

### 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!

2. Jul 31, 2008

### CRGreathouse

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

3. Jul 31, 2008

Thanks!