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

Question

1 year ago

8

years, find the standard deviation.

1 answer:

viva [34] · Answer 1 · 2023-03-29T01:48:18+03:00

The standard deviation of the average age of a breed of dog is said to be 3.69.

<h3>What is the standard deviation about?</h3>

Note that we take:

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 <em>0.84.</em>

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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