Question

The average age of a breed of dog is 19.4 years. If the distribution of their ages is normal and

Answer 1

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.

$z=\frac{x-\mu}\sigma}$, where,

z = z-score,

x = Random sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

Now we will use normal distribution table to find the z-score corresponding to 80% or $0.80$.

z-score corresponding to 0.80 is 0.845.

Upon substituting our given values in z-score formula, we will get:

$0.845=\frac{22.8-19.4}{\sigma}$

$\sigma=\frac{22.8-19.4}{0.845}$

$\sigma=\frac{3.4}{0.845}$

$\sigma=4.0236$

$\sigma\approx 4.02$

Therefore, the standard deviation is approximately 4.02 years.