Chapter 1. Tutorial: Binomial Distributions - Definition

Problem Statement

{30020,40111,52619,41510,72114,83261,10123,20371,02480,34205}
rand(0,9)
34205[9]
{Jung,Adelaja,Yajima,Fox,Modur,Jung,Adelaja,Jung,Jung,Burke}
Burke[9]
{Gupta,Jung,Jung,Jung,Hernandez,Gupta,Jung,Gupta,Gupta,Jung}
Jung[9]
{Mazzeo,Gao,Mani,Huo,Barnes,Barnes,Rodriguez,Barnes,Sanchez,Barnes}
Barnes[9]
{Barnes,BArnes,Barnes,Barnes,Ding,Ding,Barnes,Ding,Barnes,Ding}}
Ding}[9]

There are 5 conditions for a binomial distribution to be an appropriate model for a random variable:

1. There are a fixed number n of observations

2. The n observations are independent of each other.

3. Each observation falls into one of two categories which are arbitrarily called “success” and “failure”.

4. The random variable X counts the number of “success”.

5. The probability of success p is the same for all observations.

For each situation below identify the attributes of the binomial distribution (if applicable) or identify why the following is not a binomial distribution.

Step 1

questions

Count the number of heads in 5 flips of a fair coin.

Question 1

n is

Correct.
Incorrect.

Step 2

Count the number of boys in sets of identical twins.

Question 7

n is .

Correct.
Incorrect.

Step 3

Count the number of questions correct in a multiple choice quiz of 20 questions where every question has 5 possible options and you are just guessing for every question.

Question 13

n is .

Correct.
Incorrect.

Step 4

Count the number of months until an individual wins the jackpot in the Pick-4 lottery, if he buys one lottery ticket per month, and plays the same 4 numbers each time.

Question 19

n is .

Correct.
Incorrect.