Normal Calculations Presentation 1.13
Normal Calculations • There are typically two types of normal calculations. • Calculate probabilities under the curve. • Calculate scores given a probability.
Calculate Probabilities • Many times it is helpful to know the likelihood of an event occuring. • In a normal distribution, you can easily calculate such probabilities. • And not just using the empirical rule!
Calculate ProbabilitiesExample #1 • I just got my SATs back and I scored 1360. What percent of students taking the SAT did I outperform? • Given that the test scores follow the normal N(800,200), find the area to the left (below) the score 1360. Normalcdf(0,1360,800,200) =0.9974 or 99.74%
Calculate ProbabilitiesExample #1 • The previous example also demonstrates how to determine percentiles. • A percentile is simply the percent or proportion of data points that are less than or equal to the given data point. • Or…the percent of area below the given point in the distribution. • Or…the probability that a score is equal to or below the given score.
Calculate ProbabilitiesExample #2 • I am 6 feet tall, what percent of the population is taller than I am? • Given that the heights of males follow the normal N(69,2.5) – units are in inches, find the area to the right (above) the score 6 feet or 72 inches. Normalcdf(72,999,69,2.5) =0.1151 or 11.51%
Calculate ProbabilitiesExample #3 • My doctor tells me that my son is in the 80th percentile for height as a 9-year old. If he continues, and is in the 80th percentile as an adult, how tall will he be? • Given that the heights of males follow the normal N(69,2.5) – units are in inches, find the height such that 80% of the curve is at or below that height. InvNorm(.8,69,2.5) =71.0405 inches What is this height? ?
Calculate ProbabilitiesExample #4 • I need to score in the top 5% (on the verbal part of the SAT) to be admitted to Elite University, what score do I need to get? • Given that the verbal scores on the SAT follow the normal N(505,110), find the score such that 95% (if 5% above, then 95% below) of the curve is at or below that score. InvNorm(.95,505,110) =685.9339 so 686 What is this score? ?