Final answer:
The student is looking to calculate the probability of a score between two values in a normal distribution. This is done by finding z-scores and using a z-table to determine probabilities.
Step-by-step explanation:
The student's question is related to finding the probability of a score lying between two values in a normal distribution, using the mean and standard deviation of the distribution. The student provided a mean (82), a standard deviation (6), and a specific score (x=92) and mentioned a probability figure (0.4937, 0.4939), which appears to be part of the z-table values. They are seeking to find P(85 < x < 92).
To solve this, we need to calculate the z-scores for the values 85 and 92 using the formula z = (x - mean) / standard deviation. Once we have the z-scores, we can refer to the standard normal distribution tables to find the probabilities corresponding to these z-scores and then subtract the smaller probability from the larger one to find P(85 < x < 92). Additionally, drawing a graph would involve a bell-shaped curve with markings for the mean, the points corresponding to x=85 and x=92, and shading the area between these points which represents the probability we are looking for.