Final answer:
The z-score represents how many standard deviations away a value is from the mean in a normal distribution. For x=9, which is 1.5 standard deviations to the left of the mean, the z-score is -1.5.
Step-by-step explanation:
The calculation of a z-score involves understanding its definition in a normal distribution and applying that definition to the given information. In this scenario, we have a value of x=9 that is 1.5 standard deviations to the left of the mean. Since being to 'the left' of the mean indicates a value that is less than the mean, this means that the z-score is negative. Hence, the z-score correlates with the number of standard deviations given: z = -1.5.
This relationship holds true for any value and its respective standard deviation from the mean within a normal distribution. Positive z-scores indicate a value to the right of the mean, whereas negative z-scores point to a value to the left of the mean. If x equals the mean, the z-score is zero because it is not deviating from the mean at all.