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.