The distance between two villages on a map measures 6 cm. the map has a scale 1:25000.
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We have been given that the average age of a breed of dog is 19.4 years. The distribution of their ages is normal and 20% of dogs are older than 22.8 years. We are asked to find the standard deviation.
Since 20% of dogs are older than 22.8 years, so 80% of dogs are younger than 22.8.
We will use z-score formula to solve our given problem.
, where,
z = z-score,
x = Random sample score,
= Mean,
= Standard deviation.
Now we will use normal distribution table to find the z-score corresponding to 80% or .
z-score corresponding to 0.80 is 0.845.
Upon substituting our given values in z-score formula, we will get:
Therefore, the standard deviation is approximately 4.02 years.