0
$\begingroup$

An exercise reads like this...

A coin is thrown 400 times. Calculate the probability that the number of faces:

  1. Be greater than 200.
  2. Be between 180 and 220.

...and I do not know how to do so many calculations. I suppose there must be some way of calculating it more directly, perhaps with another distribution or without using one.

Could you please help me? Thank you very much.

  • 1
    As the $n$ gets to be large the binomial distribution increasingly resembles the normal distribution. This is the implication of the Central Limit Theorem. – 2017-02-25
  • 1
    You should already know the mean and standard deviation of a binomial random variable. – 2017-02-25
  • 0
    @Ian You're right! How I did not realize before? Thank you very much! – 2017-02-25

1 Answers 1

0

Given you are doing your work on a computer, just use Mathematica:

Probability[x > 200, x \[Distributed] BinomialDistribution[400, .5]]

0.480065

Probability[180 < x < 220, x \[Distributed] BinomialDistribution[400, .5]]

0.94896

This takes 0.001496 second on a Mac.

enter image description here

  • 0
    In fact forget to put a detail in the question: This exercise is a test of the year 2009, as I am preparing for a test I will have soon. But thanks for your contribution. – 2017-02-25