It has been found that the scores obtained by students follow a normal distribution with a mean of 75 and a standard deviation of 10. The top 10% end up in the university. What is the minimum mark for a student if she gets admission to the university?
The first step is to convert the percentage to the Z-score. It can be done in one of two ways.
qnorm(0.1, lower.tail = FALSE)qnorm(0.9, lower.tail = TRUE)1.28Note that if you do not specify, the default for qnorm will be lower.tail = TRUE.
Z = (X – mean)/standard deviation
X = Z x standard deviation + mean
X = 1.28 x 10 + 75 = 87.8
