Using the binomial distribution, it is found that there is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.
<h3>What is the binomial distribution formula?</h3>The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 25 students, hence n = 25.
- 70% do not commit any error, hence 30% do and p = 0.3.
The probability that at least one commits an error is given by:
In which:
Then:
There is a 0.999977 = 99.9977% probability that at least one of them makes a Type I error.
More can be learned about the binomial distribution at brainly.com/question/24863377