On an exam with a mean of M = 82, you obtain a score of X = 86. a) Would you pre

Question

On an exam with a mean of M = 82, you obtain a score of X = 86. a) Would you prefer a standard deviation of s = 2 or s = 10 (Hint: Sketch each and find the location of the score)
b) If your score were X = 78, would you prefer s = 2 or s = 10? Explain your answer
On an exam with a mean of M = 82, you obtain a score of X = 86. a) Would you prefer a standard deviation of s = 2 or s = 10 (Hint: Sketch each and find the location of the score)
b) If your score were X = 78, would you prefer s = 2 or s = 10? Explain your answer

Explanation / Answer

If you are above the mean you would prefer a lower standard deviation because that puts you in a higher percentile in the class. Assuming normal distribution, an 86 with a standard deviation of 2 gives you a z score of 2, which puts you in the top 3% of your class. If s= 10 your z score is .4 which only puts you in the top 35 %. For similar reasons, you would prefer a higher standard deviation if your score were below the mean, such as 78. You would only be in the bottom 35% of the class, instead of the bottom 3%.

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.