Question

A principle of a school notices that 390 of the 3000 student in his school scored below one standard deviation on the general test of achievement. he think that this is just a price of information he needs to persuade the superintendent that his school has an unusually high incidence of underachievers? comment on the strength of his argument.

Answer 1

As per 68-95-99.7 rule, percentage of observations within 1 standard deviation from mean is 68.27 %. So, percentage above and below one standard deviation is 100 - 68.27 = 31.73.

So, percentage below one standard deviation = 31.73/2 = 15.865 %.

Principal notices 390/3000 = 13 % below one standard deviation.

Comparison of normal distribution area of 15.865 % with the Principal's observation of 13 % shows that this figure of 15.865 % is not unusually high incidence of underachievers.

So, his argument lacks strength.