Answer: B
Step-by-step explanation:
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
Answer:
The right answer is the last option, 12,12.
Step-by-step explanation:


Answer:
One by third
Step-by-step explanation:
According to the figure the right angle triangle that was on left would be 3 times bigger than the right triangle that was on right. So here the dimension of the right triangle is one by third and equivalent to the dimension of the left triangle
the one on the left is 3 times larger than the one on the right. in other words, the right triangle's dimensions times 1/3 is equal to the left triangle's dimensions.