Do you remember the earlier study by Katz et al. that had students answer SAT{type questions without first reading the passage? Suppose that we gave out the answer sheets for our Psychology 1 exam mentioned in Exercise 6.3 but forgot to hand out the questions. If students just guessed at random, they would be expected to have a mean of 75 and a standard deviation of 7.5. The exam was taken by 100 students.

a) Among those who guessed randomly, what would be the cutoff score for the top 10 students?

b) What would be the cutoff score for the top 25% of the students?

c) We would expect only 5% of the students to score below _______.

d) What would you think if 25% of the students got more than 225 questions correct?

Exercise 6.3

Most of you have had experience with exam scores that were rescaled so that the instructor could “grade on a curve.” Assume that a large Psychology 1 class has just taken an exam with 300 four{choice multiple{choice questions. (That’s the kind of Psych 1 exam I took when I was a student—honest. And then professors recruited students to grade them.) Assume that the distribution of grades is normal with a mean of 195 and a standard deviation of 30. Use the software by Soper (http://www.danielsoper.com/statcalc3/) or similar widely available software, to calculate the answers to the following questions.

a) What percentage of the counts will lie between 165 and 225?

b) What percentage of the counts will lie below 195?

c) What percentage of the counts will lie below 225?