Standard Normal Random Variable

 In this article we shall discuss the standard normal random variable calculator. Probability is defined as chance of occurrence of a certain event when it is expressed quantitatively. A standard normal random variable calculator computes the probability of one event and depends on probability of other related events.


For an example:

If you toss a coin, will you get a head or tail? The value of a probability is a number between 0 and 1 inclusive.

                    probability of occurence



Basics Terms of Standard Normal Random Variable:



            The ending result of an experiment.


             Tossing a coin and the outcome would be someone of the two faces, H, T.

Sample space(S):

            In each number of certain trials, the set of all probable outcomes is called the sample space.

            When you roll a die, the sample space is:

                                         S = {1, 2, 3, 4, 5, 6} 
                                         S = {1…6}


           An event is the set of outcomes of a random occurrence, that is, a subset of a sample space.
Independent variables:

          Independent variable concerned with decisive the probability of obtaining one event or another based upon a single draw.                                                                       

                                    P (A and B) = P (A). P (B)

Dependent variables:

           Events are dependent means each probable outcome is related to the other. The two events A and B, the probability of obtaining simultaneously.

                                    P (A and B) = P (A). P (B|A)

Usage of the standard normal random variable calculator to solving a probability problem:

  • Identify the problem
  • Examine data
  • Report results


Examples for a Standard Normal Random Variable Calculator:


Example 1:

              Bruce is running in two races 200-yard race and a 300-yard race. The probability of winning the 200-yard race is 0.25, and the probability of winning the 300-yard race is 0.50. The probability of winning at least one race is 0.75. What is the probability that Bruce will win both races?

To find: P (A ∩ B).


Step 1:  Identify the problem.  

                    Event A = Bruce wins the 200-yard race.

                    Event B = Bruce wins the 300-yard race. 
Step 2: Examine data

                     P (A) = 0.25
                     P (B) = 0.5
                     P (A ∪ B) = 0.75

Step 3: To locate the above values in a standard normal random variable calculator:

                calculate an random variable