Question

A true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of arandomly chosen student. Find the mean score and interpret the result. Round the answers to two decimal places as needed.X5678 910P(x) 0.06 0.16 0.34 0.23 0.15 0.06Send data to ExcelThe mean isIf we were to give this quiz to more and more students, the mean score for these studentswould approach.dDdedo13

Answer 1

Solution

Question 1:

- The formula for finding the mean score is that of the expected value formula. That is,

$\begin{gathered} E(x)=\sum_{i=1}p_i\times x_i \\ where, \\ p=\text{ The probability of getting a score of }x\text{ } \\ x=\text{ The actual score} \end{gathered}$

- Thus, the mean can be gotten as follows:

$\begin{gathered} \sum px=5\left(0.06\right)+6\left(0.16\right)+7\left(0.34\right)+8\left(0.23\right)+9\left(0.15\right)+10(0.06) \\ =7.43 \end{gathered}$

The mean score is 7.43

Question 2:

- The more students write the exam, the more the mean score will approach the theoretical mean score.

- The theoretical mean score is calculated above to be 7.43

- Thus, as more students write the quiz, their scores approach 7.43