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Graphing the Standard Normal Curve The Normal Probability Distribution menu for the TI-83+/84+ is found under DISTR (2nd VARS). NOTE: The default is µ = 0 and σ = 1 The Normal Distribution functions: #1: normalpdf pdf = Probability Density Function – used to GRAPH a normal curve with the given mean and standard deviation. Syntax: normalpdf (x, mean, standard deviation) #2: normalcdf cdf = Cumulative Distribution Function – used to CALCULATE the percentage of the area given. Syntax: normalcdf (lower bound, upper bound, mean, standard deviation) #3: invNorm( inv = Inverse Normal Probability Distribution Function – this gives the x-value when given the percentile. Syntax: invNorm (probability, mean, standard deviation) To find ShadeNorm( go to DISTR and right arrow to DRAW. Choose #1:ShadeNorm(. #1:ShadeNorm( = Shading area – this allows us to calculate percentiles while looking at the area of the normal curve that the data creates. Syntax: ShadeNorm (lower bound, upperbound, mean, standard deviation) Example 1: Graph and investigate the normal distribution curve where the mean is 0 and the standard deviation is 1. Go to the Y = menu. Adjust the WINDOW. GRAPH. You will have to set your own window. Guideline is: Xmin = mean - 3 SD Xmax = mean + 3 SD Xscl = SD Ymin = 0 Ymax = 1/(2 SD) Yscl = 0 Now, the area under the curve between particular values represents the probabilities of events occurring within that specific range. This area can be seen using the command ShadeNorm(. By entering parameters -1,1 you will see the area, indicating approximately 68% probability of a score falling within 1 standard deviation from the mean in a normally distributed set of values. Example 2: Given a normal distribution of values for which µ is 70 and σ is 4.5, find: a) the probability that a value is between 65 and 80, inclusive. b) the probability that a value is greater than or equal to 75. c) the probability that a value is less than 62. d) the 90th percentile for this distribution. 1a: 1b: 1c: 1d: