Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?

Question

how to find the percentile if the average and std. deviation are given already 

Answer 1

Knowing they are normally distributed, we need to find the percentile given the value of 65. Using a TI-84 plus calculator we can use normalcdf(Lower, Upper, mean, std. deviation) to find the percentile. We are finding a percentile, so our lower limit will be -E99(a really small number), our upper limit will be 65, the mean is 70, and the std. deviation is 10. So we compute normalcdf(-E99,65,70,10)=0.3085. Thus, this score is around the 30.85th percentile.