Find the z-score for the given raw score, mean, and standard deviation. Assume a normal probability distribution

score = 15, ì = 16 , and ó = 2
Could you show me how to do this. My instructor has tried but I just don't understand how to do it and I have several questions to answer that are just like this.

z = (x-u)/s, where x is the value, u is the mean, and s is the standard deviation.

You have x = 15, u = 16, and s = 2. z =?

but wouldn't that make it a negative?

You can have a negative z score.

So anytime it is asking for a z score this is the formula to use? What if it was not normal distribution? Is their another formula?

Thank you for your help. I wish my instructor explained it that easy!

Z scores are used for finding probabilities with normal distributions.

If you cannot assume the distribution is normal, a z score would not be used.

To find the z-score for a given raw score, mean, and standard deviation, you can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case, you have a raw score of 15, a mean of 16, and a standard deviation of 2. Plugging these values into the formula, you get:

z = (15 - 16) / 2
z = -1 / 2
z = -0.5

Therefore, the z-score for a raw score of 15, a mean of 16, and a standard deviation of 2 is -0.5.

To calculate the z-score, you subtract the mean from the raw score and then divide the result by the standard deviation. The z-score tells you how many standard deviations a raw score is away from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.