Question

1. A patient recently diagnosed with Alzheimer's disease took a cognitive abilities test. The patient scored a 45 on the test (mean = 52, standard deviation = 5). What is this patient's percentile rank?
2. Another patient with Parkinson's disease took the same cognitive abilities test as in the question above and scored an 54. What percent of individuals would receive higher score?
3. A fifth grader took a standardized achievement test (mean = 125, S = 15) and scored a 148. What was this child's percentile rank?
4. Pat and Chris both took a spatial abilities test (mean = 80, S = 8). Pat scored a 76 and Chris scored a 94. What percent a individuals would score between Pat and Chris?

Answer 1

a) P(X < 45) = P(z < (45-52)/5) = P(z < -1.4) = 0.0808 (Percentile)

b) P(X > 54) = P(z > (54 - 45)/5) = P(z > 1.8) = 1 - P(z < 1.8) = 1 - 0.9641 = 0.0359
3.59% would receive a higher score

c) P(X < 148) = P(z < (148 - 125)/15) = P(z < 1.53) = 0.9370 (Percentile rank)

d) P(X < 94) - P(X < 76) = P(z < (94 - 80)/8) - P(z < (76 - 80)/8) = P(z < 1.75) - p(z < -0.5)
= 0.9599 - 0.3085 = 0.6514
Hence, 65.14% would score between Pat and Chris