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Answer :
The probability distribution that X has is a binomial distribution, and the expected score on the exam is 20.
a. The correct probability distribution is a binomial distribution.
This is because the multiple-choice exam consists of 100 questions with 5 possible responses to each question.
The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome, is known as the binomial distribution with parameters n and p in probability theory and statistics: success (with probability p) or failure (with probability q= 1 - p)
Therefore, this is a classic example of a binomial distribution where there are two outcomes in each trial (success and failure) and the trials are independent of each other.
(b) The expected score on the exam
The expected value of X is given by the formula;
Expected value (E) = np
n is the number of trials (100)
p is the probability of getting the correct answer (1/5).
Therefore, Expected value (E) = np
= 100 × (1/5) = 20
So, your expected score on the exam is 20.
A score of 50 is z = 6 standard deviations above the mean.
Therefore, it is extremely unlikely that you would score over 50 on this exam.
In conclusion, a binomial distribution is the probability that X has. Meanwhile, 20 is the expected score.
Learn more about binomial distribution here:
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