# Normal Distribution Using Excel

“I’m not an outlier; I just haven’t found my distribution yet! “
The normal distribution is symmetrical i.e. the left side is a mirror image of the right side. In other words, it has 50% of the scores below mean and 50 % above mean (Mean = Median)

Problem 1: Suppose you are asked to calculate the chances that income of a randomly selected person will be less than 3000 dollars. It is known that the income levels are normally distributed with a mean of 3500 and standard deviation of 500.

Using Excel:
1. Go to Formulas tab , then Press Insert Function button and Choose Statistical then NORMDIST from the function name , Cick Ok

2. NORMDIST function returns the normal distribution for the specified mean and standard deviation

Syntax:
= NORMDIST (value for which you want the distribution, mean, standard deviation, cumulative distribution or probability mass function)

Note: If fourth part of the above syntax is TRUE, NORMDIST returns the cumulative distribution function; if it is FALSE, it returns the probability mass function.

=NORMDIST (3000, 3250, 500, TRUE) . In this case, it returns 0.3085.

Interpretation: 0.3085 is the probability that a randomly selected person’s income is less than 3000 dollars.

Problem 2:  Suppose you are asked to calculate the income level which could be exceeded by only top earning 25 percent of people. This means to calculate the income of an individual whose percentile is 75.

Using Excel:
1. Go to Formulas tab , then Press Insert Function button and Choose Statistical then NORMINV  from the function name , Cick Ok

2. NORMINV function returns the inverse of the normal distribution for the specified mean and standard deviation

Syntax:
= NORMINV (probability, mean, standard deviation)

=NORMINV (0.75, 3250, 500). In this case, it returns 3587 dollars.

Interpretation: This means that the top earning 25 percent of people earn more than 3587 dollars.  