![]() ![]() The lowest 16% of scores are all scores less than 1100. The lowest 16% of scores are those that are more than 2 standard deviations less than the mean. The remaining 32% are more than one standard deviation from the mean. We know that 68% of the SAT scores are within one standard deviation away from the mean. So the top 2.5% of SAT scores range from 1500 to 1600 (the maximum possible score). ![]() From the symmetry of the normal curve, we know that the top 2.5% of the SAT scores the ones that are more than 2 standard deviations larger than the mean. We know that 95% of SAT scores are within two standard deivations from the mean, so 5% are greater than two standard deviations away. In the example above, we saw that SAT scores follow a normal distribution with a mean of 1100 and a standard deviation of 200. Since the normal model is symmetric, half of the test takers from part 1 (95%/2 = 47.5%) will score between 7 while the remaining 47.5% will score between 11. The x-value of the center of the bell corresponds to the population mean, which we will denote by the greek symbol \(\mu \text\)Ībout what percent of test takers score 700 to 1500?ħ represent two standard deviations above and below the mean respectively, which means about 95% of test takers score between 7. However, these curves can look different depending on the details of the model. The normal distribution always describes a symmetric, unimodal, bell-shaped curve. We say that data is normally distributed when the corresponding histogram is bell-shaped. Indeed it is so common, that people often know it as the normal curve or normal distribution. The symmetric, unimodal, bell curve is ubiquitous throughout statistics. Can you guess what it is? That's right it's the normal distribution.Īmong all the distributions we see in practice, one is overwhelmingly the most common. There is one distribution that can help us answer all of these questions. What proportion of adults have systolic blood pressure above 140? What is the probability of getting more than 250 heads in 400 tosses of a fair coin? If the average weight of a piece of carry-on luggage is 11 pounds, what is the probability that 200 random carry on pieces will weigh more than 2500 pounds? If 55% of a population supports a certain candidate, what is the probability that she will have less than 50% support in a random sample of size 200? Section 4.1 The Normal Distribution Part I Subsection Normal distribution model Hamilton Circuits and the Traveling Salesperson Problem.Euler Circuits and Kwan's Mail Carrier Problemġ6 Graph Theory: Hamilton Circuits and the Traveling Salesperson Problem.Researchers in Modeling and Applied Mathematicsġ5 Graph Theory: Introduction and Euler Paths and Circuits.Researchers in Voting Theory and Voter Representationġ4 Researchers in Modeling and Applied Mathematics. ![]()
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