Final answer:
To find the probability of a score between 600 and 750 in a normal distribution with a mean of 600 and a standard deviation of 100, calculate the z-scores and then subtract the area under the curve for the lower z-score from the area for the higher z-score.
Step-by-step explanation:
The question at hand involves using properties of the normal distribution to find the probability of a score falling between two values, given the mean and standard deviation of the distribution. In this case, a score between 600 and 750 on an exam with a mean (μ) of 600 and a standard deviation (σ) of 100.
The first step is to standardize the scores to z-scores using the formula z = (x - μ) / σ, where x is the score of interest. Next, we look up the z-scores in a Z-Table or use a calculator with normal distribution functions to determine the probabilities corresponding to these z-scores. The final step is to find the difference between these probabilities to obtain the probability of a score falling between the two standardized values.
For the example provided, we would standardize the scores 600 and 750. As 600 is the mean, its z-score would be 0. For the score of 750, the z-score would be (750 - 600) / 100 = 1.5. Using the Z-Table or calculator, we would find the area under the curve to the left of z = 0 and to the left of z = 1.5 and subtract the smaller area from the larger one to determine the probability of a score lying between 600 and 750.