Normal distribution

As you know, every distribution with mean μ and standard deviation σ can be associated to a normal or gaussian distribution with mean 0 and standard deviation 1.


This is the standard normal distribution or unit normal distribution N(0,1). The random variable associated to this distribution, Z, is called standard normal deviate.


We use a table with the values of P(Z ≤ a), a > 0, which is the area of the shaded zone.


We use this case to calculate other possibilities:

For using the table, we have to convert the variable X which follows a distribution with mean μ into a standard normal distribution.

Then, we make the change:

Then the calculus of probability is:

The binomial distribution, B(n,p), has this function of probability:

With mean and standard deviation:
If X = B(n,p) is a binomial variable, then the variable:
   approximates to N(0,1)
Exercise: If X = N(20,2), calculate:
a) P (X > 24)
b) P (21 < X < 25)
Solution: a) 0.0228; b) 0.3023

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