Final answer:
The z-score of x=3.5, given a normal distribution with mean 6.5 and standard deviation 1.5, is -2. This indicates the value is 2 standard deviations below the mean.
Step-by-step explanation:
To find the z-score for a given value from a normally distributed random variable, we use the formula z = (x - μ) / σ, where 'x' is the value, 'μ' is the mean, and 'σ' is the standard deviation of the random variable. In this case, we have a normal distribution with a mean (μ) of 6.5 and a standard deviation (σ) of 1.5. The value in question is x=3.5.
Substituting the values into the z-score formula we get:
z = (3.5 - 6.5) / 1.5
Calculating this, we find:
z = -3 / 1.5 = -2
This z-score tells us that the value x=3.5 is 2 standard deviations below the mean of the given normal distribution. A z-score of -2 indicates that the value is relatively far below the mean when considering the normal distribution of the data.