Question

Nicole missed the lesson on normal distribution and needs to do her homework. Explain to Nicole how to use the mean and standard deviation of a normal distribution to determine the top 5% of the population.

Answer 1

To determine the top 5% of the population, she needs to do a 90% confidence interval for the population. The region in the interval gives 90% of the population. The region above the interval gives the top 5% while the region below the interval gives the bottom 5% of the population.

90% C.I. = mean + or - 1.645 x (standard deviation / sqrt(sample size))

Therefore, the top 5% are the region above mean + 1.645 x (standard deviation / sqrt(sample size))