Goran is in his first semester at a university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score, which was 66. Among all the students in the course, the mean of the exam was 63 with a standard deviation of 7.Find the z-score of Goran's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places.=z
Question
Goran is in his first semester at a university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score, which was 66. Among all the students in the course, the mean of the exam was 63 with a standard deviation of 7.Find the z-score of Goran's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places.=z
Solution
To calculate the z-score, we use the formula:
z = (X - μ) / σ
where: X = Goran's score = 66 μ = Mean score = 63 σ = Standard deviation = 7
Substituting the values into the formula, we get:
z = (66 - 63) / 7 z = 3 / 7 z = 0.43
So, the z-score of Goran's exam score is 0.43. This means that Goran's score was 0.43 standard deviations above the mean score.
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