Question

Describe a probability distribution. Explain the x-axis, y-axis, and area under the

distribution.

Answer 1

Solution:  

a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Example :

This list is a probability distribution for the probability experiment of rolling two dice. We can also consider the above as a probability distribution of the random variable defined by looking at the sum of the two dice.

Suppose that we roll two dice and then record the sum of the dice. Sums anywhere from two to 12 are possible. Each sum has a particular probability of occurring. We can simply list these as follows:

• The sum of 2 has a probability of 1/36
• The sum of 3 has a probability of 2/36
• The sum of 4 has a probability of 3/36
• The sum of 5 has a probability of 4/36
• The sum of 6 has a probability of 5/36
• The sum of 7 has a probability of 6/36
• The sum of 8 has a probability of 5/36
• The sum of 9 has a probability of 4/36
• The sum of 10 has a probability of 3/36
• The sum of 11 has a probability of 2/36
• The sum of 12 has a probability of 1/36

A probability distribution can be graphed, and sometimes this helps to show us features of the distribution that were not apparent from just reading the list of probabilities. The random variable is plotted along the x-axis, and the corresponding probability is plotted along the y-axis. For a discrete random variable, we will have a histogram For a continuous random variable, we will have the inside of a smooth curve.

The Normal probability distribution curve is given below:

The total area under a normal probability distribution curve is 1 or 100%. The mean, median and mode are same in case of normal distribution and are located at the center of the normal curve. The Mean divides the normal distribution curve into two equal halves. The area to the left of mean is 50% and area to the right of mean is 50%. The empirical rule of the normal distribution says that:

• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.

So there is only 0.3% of data falls outside three standard deviations of the mean.

hope this helps!! :))