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To calculate the mean absolute deviation, you first must find the mean of the data and then find the difference between each piece of data and the mean.
Please see the attached picture for the work.
The mean absolute deviation is approximately 1.48.
This means that the numbers of candies in the 10 bags are all very close to one another. There is not much variation.
Please see the attached picture for the work.
The mean absolute deviation is approximately 1.48.
This means that the numbers of candies in the 10 bags are all very close to one another. There is not much variation.
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