This is often the most used distribution in Six Sigma.Commonly used in inferential statistics.They will never be perfect unless you have an infinite data set.Symmetrical distribution about the mean (a bell-shaped curve).
Normal Distribution is the most widely known symmetric distribution for continuous data.Statisticians refer to the normal curve as the Gaussian Probability Distribution, named after Gauss.Įntertainingly, when students ask for a professor to grade on a curve, they probably don’t know that would mean 50% of the students would receive below a 50 or less than a D! Basic Assumptions: Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.The Normal distribution is used to analyze data when there is an equally likely chance of being above or below the mean for continuous data whose histogram fits a bell curve.112 said they'd vote for Brown, 207 said they'd vote for Feliz, and 31 were undecided. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. There are two candidates for city council in an upcoming election: Brown and Feliz. The city of Raleigh has 9500 registered voters.Based on this sample, we might expect how many of the representatives to support the education bill?.Give the sample statistic for the proportion of voters surveyed who said they were supporting the education bill.Of them, 14 said they were supporting a new education bill, 12 said there were not supporting the bill, and 2 were undecided. A political scientist surveys 28 of the current 106 representatives in a state's congress.Interested readers can search for and find a lot of information on the Internet. Many controversies exist for IQ scores, and some even consider IQ scores unreliable. It should be noted that various details of IQ testing have changed from time to time, and one’s IQ score also varies over time. This implies about 1 in 1000 has an IQ of 145 or higher. Again, 145 corresponds to \(z\) = 3.0, and the table shows.In other words, less than 3 out of 100 people have an IQ score higher than 130. Similarly, 130 corresponds to \(z\) = 2.0.Since 50% is supposed to be above the average of 100 (by symmetry), this means 50 - 34.13 = 15.87 (%) has an IQ score above 115. So, by the table, 34.13% of the population has an IQ score between 100 and 115. 115 is one standard deviation above the mean, i.e., \(z\) = 1.0.100 is the average, so by symmetry, exactly 50% of the population has an IQ score of 100 or better.What are the probabilities that one’s IQ score is Suppose that IQ scores are distributed with a mean of 100 and a standard deviation of 15. This person should go see the doctor immediately. Since 100-99.38=0.62 (%), only 0.62%, i.e., less than 1% of the population, has a cholesterol level 260 or higher. Adding the 50% of those who are below average (\(z\) less than 0), this gives us 99.38% below \(z\)=2.5. The table shows that 49.38% of the people belong to the interval between \(z\)=0 and \(z\)=2.5. However, 260 mg/dl corresponds to \(z\)=2.5. In other words, about 34% of all the people have a cholesterol level between 160 and 200. According to the table, this amounts to 0.3413, or about 34%. Between 160 and 200 would correspond to the z-score between 0 and 1.
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