Normal Distribution Many things closely follow a Normal Distribution:

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Normal Probability Distributions

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Presentation transcript:

Normal Distribution Many things closely follow a Normal Distribution: Heights of people Size of things produced by machines Errors in measurements Blood pressure Marks on a test We say the data is "normally distributed".

But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this Normal Distribution

The Normal Distribution has: Symmetry about the center 50% of values less than the mean and 50% greater than the mean

Standard Deviation and Probability

Key Areas under the Curve For normal distributions + 1 SD ~ 68% + 2 SD ~ 95% + 3 SD ~ 99.9%

Standard Normal probability Distribution A random variable that has a mean 0 and SD 1 is said to have a standard normal probability distribution. This particular random variable is designated by the letter Z. The Z formula is

The z score can be defined as the number of SD that a value X is above or below the mean of distribution. If the value of X is more than mean Z score is …Positive………… If the value of X is less than mean Z score is Negative…………… If the value of X is equal to mean Z score is ……………

In a grocery store, the mean expenditure per customer is Rs 25000 with a SD of Rs.3000. If a random sample of 50 customer is selected, what is the probability that the sample average expenditure per customer is more than Rs. 26000?

1-A placement company has conducted a written test to recruit people in a software company. Assume that the test marks are normally distributed with mean 120 and SD 50. Calculate the following: Probability of randomly obtaining scores greater than 200 in this test. Probability of randomly obtaining a scores greater that is 180 or less.