normal distribution- Bhavi Shah

NORMAL DISTRIBUTION

The Normal distribution is one of the basic building blocks of statistics. The Normal distribution is also called the Gaussian distribution. Many measurements and physical phenomena can be approximated with the event distribution. The eventl Distribution has applications in many areas of business. Example, portfolio returns and human performance.

The 68, 95, 99.7 are rules for the Normal distribution states that:

68% of all observations lie within 1 standard deviation of the mean, 
within the range of µ +/- s

95% of all observations lie within 2 standard deviations of the mean, 
within the range of µ +/- 2s

99.7% of all observations lie within 3 standard deviations of the mean, 
within the range of µ +/- 3s

50% of normal distribution lies within 0.6745 standard deviations of the mean.

Normal Distribution Cumulative Distribution Function:

The Cumulative Distribution Function (CDF) of a probability distribution, evaluated at a number, is the probability that random variable will be less than or 0 and 1

 Approximates the Binomial  Distribution  when Binomial Distribution parameter p is not too close to 1 or 0.

Approximates the Poisson Distribution  when Poisson Distribution parameter λ is large. 

z score- Ekta Goraksha

Z-Scores

Sometimes we want to do more than summarize a bunch of scores. Sometimes we want to talk about particular scores within the bunch. We may want to tell other people about whether or not a score is above or below average. We may want to tell other people how far away a particular score is from average. We might also want to compare scores from different bunches of data. We will want to know which score is better. Z-scores can help with all of this.

They Tell Us Important Things

Z-Scores tell us whether a particular score is equal to the mean, below the mean or above the mean of a bunch of scores. They can also tell us how far a particular score is away from the mean. Is a particular score close to the mean or far away?

If a Z-Score….

ü      Has a value of 0, it is equal to the group mean.

ü      Is positive, it is above the group mean.

ü      Is negative, it is below the group mean.

ü      Is equal to +1, it is 1 Standard Deviation above the mean.

ü      Is equal to +2, it is 2 Standard Deviations above the mean.

ü      Is equal to -1, it is 1 Standard Deviation below the mean.

ü      Is equal to -2, it is 2 Standard Deviations below the mean.

Z-Scores Can Help Us Understand…

How typical a particular score is within bunch of scores. If data are normally distributed, approximately 95% of the data should have Z-score between -2 and +2. Z-scores that do not fall within this range may be less typical of the data in a bunch of scores.

Z-Scores Can Help Us Compare…

Individual scores from different bunches of data. We can use Z-scores to standardize scores from different groups of data. Then we can compare raw scores from different bunches of data.