IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.
Let Z be a random variable following the standard normal distribution with mean µ = 0 and standard deviation σ = 1.
The 67th percentile of the distribution is the value z that separates the bottom 67% of the distribution from the top 100% - 67% = 33%. In terms of probability, we have
Pr[Z ≤ z] = 0.67
Use the inverse CDF for the normal distribution (or lookup z scores in a table) to find
z = ɸ⁻¹(0.67) ≈ 0.4399
where ɸ(z) is the CDF for the normal distribution.