Final answer:
To earn a B in the course, Steve's average grade on the first five exams should be between 64.8 and 84.8.
Step-by-step explanation:
In order to determine the range of grades on the fifth exam that will result in Steve earning a B in the course, we need to find the minimum and maximum average grades that will satisfy the condition. Since Steve already has the grades 70, 75, 87, and 92 on the first four exams, his total points earned is 70 + 75 + 87 + 92 = 324.
To calculate the minimum average grade needed to earn a B, we assume that Steve scores the lowest possible grade, which is 0, on the fifth exam. So, his total points earned will be 324 + 0 = 324. To earn a B, the average grade should be greater than or equal to 75, so the minimum average is 324/5 = 64.8.
To calculate the maximum average grade that will still result in a B, we assume that Steve scores the highest possible grade, which is 100, on the fifth exam. So, his total points earned will be 324 + 100 = 424. To earn a B, the average grade should be less than 90, so the maximum average is 424/5 = 84.8.
Therefore, the range of grades on the fifth exam that will result in Steve earning a B is from 64.8 to 84.8.