91影视

We do not know the distribution of the scores; therefore, we will use the Chebyshev rule to find the interval.

As per the rule, 8/9 proportion, i.e., almost 89% of all the students鈥� scores, will fall under the 3rd standard deviation from the mean. Hence, we use $\stackrel{炉}{x}卤3s$to find the interval.

$$\begin{gathered} \stackrel{炉}{x}卤3s \\ Lowerrange=\stackrel{炉}{x}-3s \\ =19-3\left(65\right) \\ =19-195 \\ =-176 \\ Upperrange=\stackrel{炉}{x}+3s \\ =19+3\left(65\right) \\ =19+195 \\ =214 \end{gathered}$$

Therefore, the most likely chances are that a random student鈥檚 SAT-Math score will be anywhere from 176 below his/her previous SAT-Math score to 214 above his/her SAT-Math score.

We will be using the Chebyshev again rule due to similar reasoning,

$$\begin{gathered} \stackrel{炉}{x}卤3s \\ Lowerrange=\stackrel{炉}{x}-3s \\ =7-3\left(49\right) \\ =7-147 \\ =-140 \\ Upperrange=\stackrel{炉}{x}+3s \\ =7+3\left(49\right) \\ =7+147 \\ =154 \end{gathered}$$

Therefore, the interval where a random student鈥檚 SAT-Verbal score might fall is 140 below his/her previous score to 154 above his/her previous score.

An increase of 140 points for SAT-Math would be a little less than 2 standard deviations from the mean, whereas a 140 point increase in SAT-Verbal would be a little less than 3 standard deviations from the mean. As a 140 point change in SAT-Math is not as large as a 140 point change in SAT-Verbal, it is most likely an SAT-Math score.