Final answer:
To calculate the probability that standardized test takers scored between 450 and 500, calculate the z-scores for both scores and use the z-table. To find the percentage of test takers who scored 450 or more, calculate the z-score for 450 and subtract its cumulative probability from 1. For the percentage of test takers who scored 600 or less, calculate the z-score for 600 and find its cumulative probability.
Step-by-step explanation:
To calculate the probability that the standardized test takers scored between 450 and 500, we need to calculate the z-scores for both scores and then use the z-table to find the probability. The z-score for 450 is calculated as (450 - 500) / 70 = -0.714. The z-score for 500 is calculated as (500 - 500) / 70 = 0. The probability of scoring between 450 and 500 is the difference between the cumulative probabilities for these z-scores: P(450 < x < 500) = P(z < 0) - P(z < -0.714).
To calculate the percentage of standardized test takers who scored 450 or more, we need to calculate the z-score for 450 and find its cumulative probability using the z-table. The z-score for 450 is -0.714, and P(z < -0.714) gives us the percentage of test takers who scored less than 450. To find the percentage who scored 450 or more, we subtract this value from 1.
To calculate the percentage of standardized test takers who scored 600 or less, we need to calculate the z-score for 600 and find its cumulative probability using the z-table. The z-score for 600 is (600 - 500) / 70 = 1.429, and P(z < 1.429) gives us the percentage of test takers who scored less than 600. To find the percentage who scored 600 or less, we can simply multiply this value by 100.