Assume that a procedure yields a binomial distribution with a trial repeated n30 times. Use the binomial probability formula to find the probability of x5 successes given the probability p of success on a single trial. Round to three decimal places.

The probability is , in which p is the probability of a success on a single trial.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The trial is repeated 30 times:

This means that

Find the probability of 5 successes given the probability p of success on a single trial

This is . So

The probability is , in which p is the probability of a success on a single trial.

x= 149. 24+7=31. 180-31=149

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