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WS #23 Normal Distributions Solving Problems with the Add-in Program NORMDIST Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100), that is, the mean is 500 and the standard deviation is 100. What is the probability a student scored between 400 and 650? Key Strokes PGRM Display/Comment Brings up the Add-in Program Menu 3 ENTER Shows the option for two types of problems. We will select 1 because our problem gives us the interval (400, 600) and asks for the % of individual students in that interval. 1 ENTER The program asks for the lower bound of the interval which is 400. 400 ENTER The program asks for the upper bound of the interval which is 650. 650 ENTER The program now asks for the mean of the normal distribution which is 500. www.mikeshoreline.com 5/7/2017 WS 23 Page 1 of 6 500 ENTER The program now asks for the Standard Deviation of the normal distribution which or the Standard error of the sampling distribution. Since this is a population distribution, the proper entry is 100. 100 ENTER The program gives the answer: The probability the student scored between 400 and 650 is 0.7745% www.mikeshoreline.com 5/7/2017 WS 23 Page 2 of 6 Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100), that is, the mean is 500 and the standard deviation is 100. What percent of individuals scored less than 300? Key Strokes PRGM 3 ENTER Display/Comment The interval we are looking for is (- , 300). Since the calculator does not have the symbol, we have to use the smallest number in the calculator which is 1 10 99 or -E99. The calculator interval is (-E99, 300). We select 1. 1 ENTER - 2ND EE 99 ENTER 300 ENTER 500 ENTER 100 ENTER The probability a student scored less than 300 is .0228. www.mikeshoreline.com 5/7/2017 WS 23 Page 3 of 6 Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100), that is the mean is 500 and the standard deviation is 100. What score would it take to be in the in the top 10% of all students. Key Strokes PGRM 3 ENTER Display/Comment The top 10% is the rightmost 10% area.. We are given an area, and we need to find the right bound on the x-axis We select 2. 2 ENTER The area from the left is 100-.10 = 0.90 0.90 ENTER 500 ENTER 100 ENTER The score required is 628.1552. Any score above this number will be in the top 10% of all scores. www.mikeshoreline.com 5/7/2017 WS 23 Page 4 of 6 Solving Problems with the TI-38 built in programs: NORMALCDF and INVNORMAL Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100), that is, the mean is 500 and the standard deviation is 100. What percent of students had scores less that 750. When we know the interval (, 750) and want the area above it, we use the Normalcdf command. This command takes the form of Normalcdf (lower bound, upper bound, mean, standard deviation). The TI-83 has no symbol or negative or positive infinity, or , so we use 10 99 for negative infinity and 10 99 for positive infinity. These are the smallest and largest numbers the TI 83 will take. Key Strokes nd Comment 2 DISTR Displays the Distribution Menu 2 Enter Displays the normalcdf on the home page Enters the parameters for the command - 2nd EE 99 , 750 , 500, 100 ) Enter Displays the answer 0.9938. This means that 99.38% of the test scores are lower than 750. Problem: Given the SAT distribution of N(500, 100), what score would it take to get into the top 10% of all tests. To be in the top 4% of the tests would require a score above the 96th percentile. For this problem, we use the invNoraml command. This command takes the form invNormal (percentile, mean, standard deviation). www.mikeshoreline.com 5/7/2017 WS 23 Page 5 of 6 Key Strokes Comment nd 2 Distr 3 0.96 , 500, 100, ) Enter Add the proper parameters to the command Display : A test score of 675.069 will be above 96 percent of all tests taken and in the top 4% of all tests. www.mikeshoreline.com 5/7/2017 WS 23 Page 6 of 6