Using the binomial distribution, it is found that there is a:
a) 0.9298 = 92.98% probability that at least 8 of them passed.
b) 0.0001 = 0.01% probability that fewer than 5 passed.
For each student, there are only two possible outcomes, either they passed, or they did not pass. The probability of a student passing is independent of any other student, hence, the binomial distribution is used to solve this question.
<h3>What is the binomial probability 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:
- 90% of the students passed, hence
.
- The professor randomly selected 10 exams, hence
.
Item a:
The probability is:
In which:
Then:
0.9298 = 92.98% probability that at least 8 of them passed.
Item b:
The probability is:
Using the binomial formula, as in item a, to find each probability, then adding them, it is found that:
Hence:
0.0001 = 0.01% probability that fewer than 5 passed.
You can learn more about the the binomial distribution at brainly.com/question/24863377