Question

A normal distribution has a mean of 143 and a standard deviation of 12.7.

What is the z-score of 165?

1.62

1.73

1.87

2.04

Answer 1

z-score for a value of 165 is + 1.73 times the standard deviation

The correct answer is B. 1.73

Explanation:

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

Mean of the normal distribution = 143

Standard deviation = 12.7

2. What is the z-score of 165?

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, 165 will have the following z-score:

165 - 143 = 22 and it's above the mean.

Now, we calculate the z-score, using the value of the standard deviation this way:

22/12.7 = 1.73

z-score for a value of 165 is + 1.73 times the standard deviation

The correct answer is B. 1.73