Final answer:
To calculate the student's z-score, the formula (X - μ) / σ is used, resulting in a z-score of 1.5 which indicates the student's performance is significantly above the mean IQ score of the group.
Step-by-step explanation:
To find a student's z-score in an IQ test where the average score is 70 and the standard deviation is 10, and the student's score is 85, we use the formula for calculating a z-score: z = (X - μ) / σ, where X is the individual score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get z = (85 - 70) / 10 = 15 / 10 = 1.5. This means the student's score is 1.5 standard deviations above the mean.
A z-score is useful because it allows us to compare individual scores to the average within the same dataset or even across different datasets with different averages and standard deviations. The z-score tells us how many standard deviations an individual score is from the average. In the IQ test scenario, a z-score of 1.5 indicates that the student's performance is significantly above average.