in a population of normally distributed aptitude scores of 1000 academy students with mean 70 and standard deviation 10, how many score above 95? Is it 250?

Answer 1

We obtain the Z-score for 95 with the formula Z = (x-mu)/st dev. In this case, Z = (95-70)/10 = 2.5. This means that a score of 95 is 2.5 standard deviations from the mean. From the z-tables, this corresponds to a right-tailed area of 0.0062, meaning the percent of students who score more than 95 is only 0.62%. In the context of 1000 students, approximately 6 of them score above 95.

Hope this helped!