Question

On a nationwide test by high school students, the mean score was 52 and the standard deviation was 11. The scores were normally distributed. Complete the following statements ( Choose the correct answers(68%,75%,95%,99.7%)

Answer 1

Recall that, according to the empirical rule:

1.- About 68% of the data falls within 1 standard deviation.

2.- About 99.7% of the data falls within 3 standard deviations.

Now, notice that:

`\begin{gathered} 52-11=41, \\ 52+11=63. \end{gathered}`

Therefore, approximately 68% of the students scored between 41, and 63.

Now, notice that:

`\begin{gathered} 52+3(11)=85, \\ 52-3(11)=19. \end{gathered}`

Therefore, approximately 99.7% of the students scored between 19 and 85.

Answer:

Approximately 68% of the students scored between 41, and 63.

Approximately 99.7% of the students scored between 19 and 85.