Answer :
Final answer:
To find the numerical limits for a D grade in a normally distributed set of psychology test scores, we calculate the scores at the 75th and 9th percentiles, resulting in rounded limits of 55 and 73, respectively.
Explanation:
The question involves finding the numerical limits for a D grade in a psychology test where scores are normally distributed with a mean of 66.9 and a standard deviation of 9. A D grade falls below the top 75% and above the bottom 9% of scores. To determine these limits, we refer to the standard normal distribution properties, where a score falling at the 75th percentile and the 9th percentile are of interest.
To find the scores corresponding to these percentiles, we use the standard normal distribution and z-scores. The formula for converting a percentile to a score in a normal distribution is Score = mean + (z * standard deviation). For the 75th percentile, the z-score is approximately 0.675, and for the 9th percentile, the z-score is approximately -1.34. Plugging these into the formula yields the scores for the D grade boundaries.
For the 75th percentile: Score = 66.9 + (0.675 * 9) = 73.075. For the 9th percentile: Score = 66.9 + (-1.34 * 9) = 54.74. Therefore, the numerical limits for a D grade, rounded to the nearest whole number, are 55 at the bottom and 73 at the top.
