# Cal Poly STAT 218 - Normal distributions (3 pages)

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## Normal distributions

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## Normal distributions

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3
School:
California Polytechnic State University
Course:
Stat 218 - Applied Statistics for the Life Sciences
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Stat 218 Day 7 Normal distributions Many phenomena especially physical measurements follow a bell shaped curve A variable that follows a symmetric bell shaped curve is said to have a normal distribution A normal distribution is characterized by two values its mean and standard deviation The mean indicates where the center and peak of the distribution are The standard deviation is the distance from the mean to where the curvature changes Example For the three normal curves below take a guess for its mean and standard deviation 40 50 60 70 80 90 100 The total area under a normal curve is one The area under the curve over a certain region indicates The proportion of values in that region The probability that a randomly selected observational unit will be in that region To find the area under the curve over a certain interval we Standardize by subtracting the mean and dividing by the standard deviation i e find a zscore Use the table of standard mean 0 std dev 1 normal probabilities which gives the area under the curve to the left of that value Or you can use the Java applet called normal probability calculations Or you can use Minitab Calc Probability distributions Normal cumulative probability Advice Always draw a sketch of the normal distribution and shade the area corresponding to the probability proportion of interest Example SAT and ACT cont Recall that scores on the SAT exam are normally distributed with mean 1000 and std dev 180 while scores on the ACT exam are normally distributed with mean 21 and std dev 6 a Draw sketches of these two distributions Label the scales as accurately as possible b Suppose that Bobby scores 1180 on the ACT and Kathy scores 30 on the ACT Determine what percentage of students score below each of these scores on the respective exams Is your answer for Bobby consistent with what the empirical rule revealed c Suppose that Peter scores 910 on the SAT and Kelly scores 15 on the ACT Determine what percentage of students score below each of

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