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18 April, 06:13

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

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  1. 18 April, 06:30
    0
    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
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