The ages of dogs at an animal shelter are normally distributed with a mean of 3.9 years and a standard deviation of 1.2 years.

What is the age of a dog at the shelter with a z-score of - 1.7?

1.86 years

2.98 years

3.23 years

5.43 year

The correct answer is A. 1.86 years

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of the dogs at an animal shelter = 3.9 years

Standard deviation = 1.2 years

2. What is the age of a dog at the shelter with a z-score of - 1.7?

Let's recall that z-score in a normal distribution, positive or negative, is the number of times of the standard deviation a certain element is from the mean. If the element is below the mean, then the z-score is negative and if it's above the mean, then the z-score is positive.

Therefore, a z-score of - 1.7 for the ages of dogs is:

-1.7 * 1.2 = - 2.04

Now, we calculate the value using the mean, this way:

3.9 + - 2.04 = 3.9 - 2.04 = 1.86

The correct answer is A. 1.86 years