This is off in two ways.
First of all this is a confidence interval.
It's NOT a probability interval.
The person who asked that has it confused.
What they are trying to ask is a binomial problem.
Second error, I think you want plus and minus 1.96, or maybe not?
If you meant 1.96 then the coverage is 95 percent and they
want to ask a binomial question where you want at least 4 successes in 5 trials, with 'p'=.95.
But you can look up the probability that a standard normal is between -.96 and 1.06, too.
However this is really not a probability statement, that's why we coin the word confidence.
NOW a prediction interval is a probability statement since it is guessing at a rv.
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