# Week 3 DQ1 – Data Analysis and Business Intelligence |Westcliff University

## Wk3 DQ1| Discussion Question 1 |Checked by Turnitin

What are the differences between Binomial Distribution and Poison Distribution?

A recent CBS News survey reported that 67% of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 15 adults.

a. How many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation?

b. What is the likelihood that exactly eight adults would indicate the Treasury should continue making pennies?

c. What is the likelihood at least eight adults would indicate the Treasury should continue making pennies?

Ans:

In the third week of our course, we discussed the various concepts of probability which included probability distribution as well. A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range (Kenton, 2018). This week 3 DQ 1 is mainly focused on the types of probability distribution (Binomial Distribution and Poison Distribution) along with a numerical analysis.

Difference between Binomial Distribution and Poison Distribution

Binomial distribution is defined as one of the types of probability distribution in which the probability of repeated number of trials is studied. Poisson Distribution is defined as one of the types of probability distribution which gives the count of independent events occurs randomly with a given period of time (S, 2016).

 Basis Binomial Distribution Poison Distribution Definition Binomial distribution is defined as one of the types of probability distribution in which the probability of repeated number of trials is studied. Poisson Distribution is defined as one of the types of probability distribution which gives the count of independent events occurs randomly with a given period of time. Nature It is Biparametric in nature which indicates that it is featured by two parameters ‘n’ and ‘p’. It is Uniparametric in nature which indicates that it is featured by only one parameter ‘m’. Outcomes In case of binomial distribution, there are only two possible outcomes (success or failure). In case of poison distribution, there are unlimited numbers of possible outcomes. Mean and Variance In case of binomial distribution, Mean is greater than Variance. In case of poison distribution, Mean is equal to Variance. BusinessApplications Binomial Distribution can be used by Banks and other financial institutions to determine the likelihood of borrowers defaulting and figuring out how much money to keep in reserve, or how much to loan. Poison Distribution can be used by service industries to predict customer sales on particular days of the year as well as can be useful in estimating demand and supply. Example Tossing a Coin (Outcomes: Head or Tail) Number of people using ATM located outside the XYZ office.(Outcomes: Unlimited) Formula P (X) = nCx px qn-x P(X) = µx e– µ/x!

Numerical Solution:

Given Information;

• Number of trails (n) =15
• Probability of Success (p) = 0.67
• Probability of failure (q) = 1-p = 1- 0.67 = 0.33

• Expected Value = 15*0.67 = 10.05(approx. 10)

Therefore, the expected value is 10 which indicate that the Treasury should continue making pennies.

• Standard deviation (σ) = √nπ (1−π) = √15×0.67(1−0.67) =1.82

Hence, the standard deviation is 1.821.

As per the binomial distribution;

• P(x = 8) = nCx .pxqn-x15C8*0.67^8*0.33^15-8

=0.1113

Therefore, the likelihood that exactly eight adults would indicate the Treasury should continue making pennies is 0.1113.

• P (X≥8) = 1−P(X<8) =1−P (X≤7) =1-0.0837 = 0.91629

Therefore, the likelihood that at least eight adults would indicate the Treasury should continue making pennies is 0.91629.

# References

S, S. (2016, May 10). Difference Between Binomial and Poisson Distribution. Retrieved from Key Differences: https://keydifferences.com/difference-between-binomial-and-poisson-distribution.html ## Author: Smirti

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