Standard deviation and above average question?

Question

A student wants to be among the top 5% in his class. the mean is 140 and standard deviation is 14. What is the minimum score he needs to get to meet his goal?
Please show me how to do this.

A student scored 150 on his midterm. The mean is 160 and standard deviation is 14. what % of student score above that student?

Answer 1

Go to your friendly Z-table and look up the Z statistic for the Z corresponding to the 95th percentile of the standard normal dist (probably about 2). Then min score= 140+ Z*14.

The students score is at the mean - 5/7 sd. [mean-1 sd = 146]. Check the table for mean-5/7 sd to get the percentile (about 30%).