We appreciate your visit to Which of the following scores on a Calculus test with a mean of 73 and a standard deviation of 17 is unusual A A score. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The score of b. 105.6 on the Calculus test is unusual.
Explanation:
To determine which score on a Calculus test is unusual, we need to calculate the z-scores for each of the given scores and compare them to the mean and standard deviation. A z-score measures how many standard deviations a data point is from the mean.
The formula to calculate the z-score is: Z = (X - μ) / σ, where Z is the z-score, X is the data point, μ is the mean, and σ is the standard deviation.
For the score of 37.5, the z-score is (37.5 - 73) / 17 ≈ -2.00. For the score of 105.6, the z-score is (105.6 - 73) / 17 ≈ 1.91. For the score of 103.9, the z-score is (103.9 - 73) / 17 ≈ 1.76. For the score of 105.6, the second time, the z-score is (105.6 - 73) / 17 ≈ 1.91. For the score of 39.3, the z-score is (39.3 - 73) / 17 ≈ -1.95.
An unusual score is typically one that falls more than 2 standard deviations away from the mean. In this case, the score of 105.6 has a z-score of approximately 1.91, which is not unusual. The other scores have z-scores beyond 2, making them unusual. However, since the question asks for "which" score, it's important to note that the score of 105.6 (the second instance) is unusual among the options provided.
In conclusion, the score of b. 105.6 on the Calculus test is unusual based on the z-scores calculated.
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