Assume the random variable X is normally distributed with mean = 50 and standard deviation a = 7. Find the 67th percentile

Question

Assume the random variable X is normally distributed with mean = 50 and standard deviation = 7. Find the 67th percentile

1. The 67th percentile is ____

( Round to two decimal places as needed)

Answer 1

To find this percentile, we first need to determine how many standard deviations this is away from the mean. We do this using a z-score table or normal distribution function on a calculator. This gives a z-value of 0.44.

Then, P₆₇ = zσ + µ = 0.44•7 + 50 = 53.08.