Solve the normal distribution IQ quiz in Python and R

In statistics, the normal distribution, or Gaussian distribution, is a type of continuous probability distribution for a real valued random variable. Normal distributions are important in statistics, and are often used in natural and social sciences to represent real valued random variables whose distributions are not known.

The normal distribution makes the shape of the bell curve, as seen below:-

The formula for the normal distribution can be seen below:-

The normal distribution’s importance is partly due to the central limit theorem, which states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance, is itself a random variable, whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal.

In this post I have taken an example about intelligence quotients (IQ’s), which take the shape of a normal distribution, and have endeavoured to use the…