Normal Distributions and Standard Scores The table below shows the average weight (in kilograms) and standard deviation of U.S. males from birth until 12 months. Using the information you learned about properties of the normal distribution, standard deviations, and z-scores to find the answers to the following problems. 1. Tommy is 3 months old and weighs 6.41kg. What percentage of males, at his age, weigh more than him. 2. Paul is 11 months old and weighs 10.02kg. What percentage of males, his age, weigh more than him? Summary statistics: Column n Mean Variance Std. dev. Std. err. Media n Age in Months 15 6.5333333 19.516667 4.4177672 1.1406626 6.5 Mean Weight (kg) 15 7.7126667 5.6360067 2.3740275 0.61297127 8.16 SD 15 0.12133333 0.00021238095 0.014573296 0.0037628088 0.12 Range Min 13.5 0 Max 13.5 Q1 Q3 2.5 10.5 7.2 3.53 10.73 5.67 9.84 0.04 0.11 0.15 0.11 0.13 Source: StatCrunch 3. A recently diagnosed patient with Alzheimer's disease takes a cognitive abilities test. The patient scores a 54 on the test (mean = 52, standard deviation = 5). What percent of individuals would receive a higher score? 4. A fifth grader takes a standardized achievement test (mean = 125, sd = 15) and scores a 148. What is this child's percentile rank? 5. Pat and Chris both took a spatial abilities test (mean = 80, sd = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris