Question

A teacher assigns a score from 1 to 4 to each student project. the table below shows the probability distribution of the scores for a randomly selected student. which score is most likely? probability distribution score: x probability: p(x) 1 0.06 2 0.20 3 0.48 4 0.26 1 2 3 4

Answer 1

The generalization of the weighted average is the expected value of a distribution. The score that is most likely to occur is 3.

How to find the mean (expectation)?

The generalization of the weighted average is the expected value of a Probability distribution. It is given by the formula,

$Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i$

As we need to calculate the score that is most likely to occur, therefore, we need to calculate the expected value of the given probability distribution, therefore, the expected value can be written as,

$E(x) = \sum xP$

where x is the score and P is the probability of the score occurring.

$E(x) = (1 \times 0.06)+(2 \times0.20)+(3 \times 0.48)+(4 \times 26)\\\\E(x) = 2.94$

Since 2.94 is the most expected value to occur which is close to 3, therefore, the score that is most likely to occur is 3.

Also, the probability of score 3 coming is maximum which is equal to 0.48.

Hence, the score that is most likely to occur is 3.

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