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In a large section of a statistics​ class, the points for the assignment are normally​ distributed, with a mean of 68 and a standard deviation of 9. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the assignment that would qualify a student for an​ A, a​ B, a​ C, and a D

User Bglbrt
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Final answer:

To find the minimum scores for an A, B, C, or D in the statistics class, we use the normal distribution to find the corresponding z-scores for each percentile rank and then convert these z-scores to actual scores using the mean of 68 and a standard deviation of 9.

Step-by-step explanation:

To find the lowest score on the assignment that would qualify a student for an A, B, C, or D in a statistics class where the assignment points are normally distributed with a mean of 68 and a standard deviation of 9, we can use the concept of z-scores and the normal distribution.

Steps to Determine the Qualifying Scores

  1. Identify the percentile rank for each grade category (top 10% for A, next 20% for B, middle 40% for C, next 20% for D).
  2. Use standard normal distribution tables, computers, or calculators to find the z-score that corresponds to each percentile rank.
  3. Convert the z-scores to actual scores using the given mean (68) and standard deviation (9).

The formula to convert a z-score to an actual score is: X = μ + (σ × z), where X is the actual score, μ is the mean, σ is the standard deviation, and z is the z-score.

Calculating the Lowest Qualifying Scores

  • For an A (top 10%): a z-score approximately 1.28 would be used.
  • For a B (next 20%): a z-score approximately 0.84 would be used.
  • For a C (middle 40%): two z-scores approximately -0.25 and 0.25 bracket the middle 40%.
  • For a D (next 20%): a z-score approximately -0.84 would be used.

After calculating, we will get the respective scores for A, B, C, and D which are the minimum scores needed to qualify for these grades.

User Staticman
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