Find the standard deviation.

Question

The average age of a breed of dog is 19.5 years. If the distribution of their ages is normal and 20% of dogs are older than 22.6 years, find the standard deviation.

Answer 1

x = dog age is normally distributed with mean 19.5 and unknown standard deviation.

z = (x - mean)/SD is distributed N(0,1) - mean o standard deviation 1 (standard normal)

If 20% of dogs older than 22.6 years, then 22.6 years is the 80th percentile,

z corresponding to 80th percentile (from standard normal table) s 0.84.

plugging z, x = 22.6 and mean = 19.5 into above z equation:

0.84 = (22.6 - 19.5)/SD

SD = (22.6 - 19.5)/0.84 = 3.69