standard deviation

Question

A state university has no French course, instead places all freshmen scoring at least 60 on a proficiency exam (Mean=50, Standard Deviation =10) to an advanced composition course. If the scores are normally distributed and there are 2500 entering freshmen, how many will be put into the advamced course?

Answer 1

A normal distribution implies mean=median. For a normally distributed population, 68% of the population will lie within 1 standard deviation on either side of the mean (34% on each side). If you go out to 2sd on either side, that will include 95% of the population. For 3sd on either side, you cover 99.7% of the population. 

 

In this case, you wish to know what percentage of the population is above 60 which is 1sd above the mean. This is also called the right-hand tail. Because we know the first standard deviation from the mean is 34% on each side and the fact that the mean=median which is at exactly 50th percentile of the population, we know that the percentage of the population scoring below 60 is 50+34=84%. That means 100-84=16% of the people scored above 60.