Question

A true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of a randomly chosen student. Find the mean score and interpret the result. Round the answers to two decimal places as needed. x 5 6 7 8 9 10 Px 0.07 0.17 0.38 0.21 0.1 0.07

Answer 1

Answer:

The mean score is 7.31. This means that each time the student takes this test, he is expected to get a score of 7.31.

Step-by-step explanation:

We have these following probabilities:

A 0.07 = 7% probability that the student scores 5 points.

A 0.17 = 17% probability that the student scores 6 points.

A 0.38 = 38% probability that the student scores 7 points.

A 0.21 = 21% probability that the student scores 8 points.

A 0.1 = 10% probability that the student scores 9 points.

A 0.07 = 7% probability that the student scores 10 points.

Mean score

We multiply each score by it's probability. So

$M = 0.07*5 + 0.17*6 + 0.38*7 + 0.21*8 + 0.1*9 + 0.07*10 = 7.31$

The mean score is 7.31. This means that each time the student takes this test, he is expected to get a score of 7.31.

Answer 2

Answer:

Mean score of the given data is 7.31.

Step-by-step explanation:

We are given that a true-false quiz with 10 questions was given to a statistics class.

Following is the probability distribution for the score of a randomly chosen student;

           X                            P(X)                                 $X \times P(X)$

            5                            0.07                                    0.35

            6                            0.17                                     1.02

            7                            0.38                                    2.66

            8                            0.21                                     1.68

            9                            0.10                                      0.9

           10                           0.07                                     0.7

                                    $\sum P(X)$ = 1  

Firstly, it should be noted that the sum of probabilities, P(X) must be equal to 1.

Now, mean score is given by the following formula;

Mean, E(X) = $\sum X \times P(X)$  {i.e. multiplying each score with the respective probability}

Mean, E(X) = 0.35 + 1.02 + 2.66 + 1.68 + 0.9 + 0.7

                   = 7.31

So, the mean score is 7.31.

The interpretation of this score is that when the student takes a true-false quiz with 10 questions, he will on average is expected to get a score of 7.31.