Statistics And Probability

Step 1: Review of Mean and Variance Formulas
For a binomial distribution with parameters

n

and

p

, the mean and variance are expressed as:

%5Cmu%20%3D%20np%2C%20%5Cquad%20%5Csigma%5E2%20%3D%20np(1%20-%20p)

Step 2: Formulating the Equations
We are provided with the following equations:

np%20%3D%2018%2C%20%5Cquad%20np(1%20-%20p)%20%3D%2012

By dividing the second equation by the first:

(1%20-%20p)%20%3D%20%5Cfrac%7B12%7D%7B18%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D

which simplifies to:

p%20%3D%20%5Cfrac%7B1%7D%7B3%7D

Step 3: Solving for $n$
Substitute

p%20%3D%20%5Cfrac%7B1%7D%7B3%7D

into the first equation:

n%20%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%20%3D%2018

Solving for

n

n%20%3D%2018%20%5Ctimes%203%20%3D%2054

Chapter Questions
1 MCQs