Question

Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 15 students who have recently taken the test. (Round your probabilities to three decimal places.)

Suppose that a student who does not receive a special accommodation is allowed 3 hours for the exam, whereas an accommodated student is allowed 4.5 hours. What would you expect the average time allowed the 15 selected students to be? (Round your answer to two decimal places.)

Answer 1

Expected number of students with accommodations is np = 15*0.04 = 0.6.

Thus, the expected number of students without accommodations is 14.4.

Use this information to find the expected number of hours all 15 students combined.

Total time for all students = (0.6)(4.5) + (14.4)(3) = 2.7+43.2 = 45.9

Now, divide by the total number of students to receive the average number of hours per student.

Average time per student = Total time for all students / Total number of students = 45.9/15 = 3.06

Thus, the expected average time per student is 3.06.