Question

On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11

The scores were normally distributed. Complete the following statements.

(a) Approximately ?% of the students scored between 40 and 62 .
(b) Approximately 95% of the students scored between ? and ?

Answer 1

a) 68%

b) 29 and 73

Explanation:

As the scores are normally distributed so, according to empirical rule the percentage of data falls within one,two and three standard deviations are 68%,95% and 99.7% respectively.

a)

mean-sd=51-11=40, mean+sd=51+11=62

The data falls within one standard deviation is 68% and so, approximately 68% of students scored between 40 and 62.

b)

The empirical rule demonstrates that 95% of scores falls within two standard deviation.

mean-2*sd=51-2*11=51-22=29

mean+2*sd=51+2*11=51+22=73

So, approximately 95% of students scored between 29 and 73.