### Probability distribution of marks should not be normal.

**What type of variable is the mark, discrete or continuous?**

Marks is a discrete random variable that has a finite number of values or a countable number of values.

A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions.

**Requirements for a Probability Distribution**

1. ΣP(x) = 1 where x assumes all possible values of marks

2. 0 ≤ P(x) ≤ 1 for every individual value of x

For example, 2000 students gave exams with full marks of 10, the probability distribution of marks to have a normal like curve will have following frequency distribution given in the table.

Marks xFrequency

*f*Probability P(X=x)040.0021230.01152990.049532270.113543990.199554970.248563900.19572510.12558840.0429220.0111040.002

import matplotlib.pyplot as plt import random import numpy as np from collections import Counter, OrderedDict fig, ax = plt.subplots(1, 1) od = OrderedDict([(0.0, 4), (1.0, 23…