The standard deviation of the average age of a breed of dog is said to be 3.69.
What is the standard deviation about?
Note that we take:
- x = dog age has mean 19.5
- Unknown standard deviation.
Hence:
z = (x - mean) /SD is distributed N (0,1) - mean o standard deviation 1 (standard normal)
Since 20% of dogs are known to be older than 22.6 years:
So 22.6 years is said to be 80th percentile,
Since z matching to 80th percentile (using the standard normal table) s is 0.84.
Then one need to plug z, x which is = 22.6
mean = 19.5 into the stated z equation:
Hence,
0.84 = (22.6 - 19.5)/SD
SD = (22.6 - 19.5)/0.84
= 3.69
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