The sample mean and standard deviation of a test of all students are 60 and 12 points, respectively. Assume there are 15,000 students, approximately how many of them have a score lower than 48?

Answer 1

Feel free to see the attached video. I included a standard negative Z-Table, and a graph of the normal curve with reference to Chebychev's Rule, to help demonstrate our output. You will see that to the left of -σ on the x-axis (-12 in our case) the total area has to be just about 15-16%, which is in line with our answer.

Multiply the P(X<48) times the # of students to get your final answer (rounded to nearest value): 2381 Students!