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Data Science Interview Handbook

Normal and Binomial Distribution

Understand the characteristics of normal distribution and binomial distribution, including their formulas and applications. Learn to calculate probabilities for discrete events and interpret the significance of mean and standard deviation in data science problems.

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Normal distribution

Normal distribution is also known as Gaussian distribution. It is symmetric and bell-shaped. It is characterized by the mean and standard deviation. See the example below.
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The highest point in the curve is the mean. Normal distribution approaches zero for very large or small values, but never touch zero. The standard deviation represents the width of the bell-shaped curve.

Quiz: Normal distribution

1.

Mark the correct option for a normal distribution.

A.

Mean > Median

B.

Mean < Median

C.

Mean == Median

D.

Undetermined

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Binomial distribution

Binomial distribution is used for discrete random variables. It counts with binary data. If we can convert the outcome into two categories (success and failure), we can use the binomial distribution to solve the problem.

For binomial distributions, two conditions need to be met:

  • The probability of success remains the same.
  • Trails are independent of each other.

To get success in an n-trial, we need:

  • Trails with two possibilities
  • Number of trials, n
  • Number of successes, k

P(k)=n!k!(n−k)!pk(1−p)n−k P(k) = \frac{n!}{k!(n-k)!}p^k(1-p)^{n-k} ...