image Chapter 6 Case Study: SAT Scores and AP Exam Scores.

The College Board reported in 2013 that females taking the Writing SAT had a mean score of with a standard deviation of , whereas males had a mean score of with a standard deviation of . Assume both sets of scores follow a normal distribution. Use this information for Exercises 44–48.

Question 6.390

45. Suppose students are identified as at-risk writers if they score below 400 on the Writing SAT.

  1. Calculate the proportion of females who will be identified as at-risk writers.
  2. Compute the percentage of males who will be identified as at-risk writers.
  3. Compare your answers to (a) and (b). Explain why this makes sense, given the values of and .

6.5.45

(a) 0.2033 (b) 0.2389 (c) A higher proportion of males will be identified as at-risk writers than females. This makes sense given that females have a higher average on the Writing SAT test than males.