Utilizing statistical probability models, you will be able to evaluate and analyze business data under uncertainty conditions

Data Analysis and Business Analytics

Response

What is a random variable?

A random variable is normally written as "x" which is a value that is determined by a random experiment's outcomes.  A random variable can be discrete or continuous. If “x” is countable it is discrete variable, if “x” is not countable it is continuous variable.

How would you differentiate a discrete from a continuous random variable?

A discrete random variable takes on only a countable number of diverse values. Values include outcomes such as 0,1,2, and so on. On the other hand, a continuous random variable usually deals with measurements it takes many values. Examples of continuous variables include height, weight, among others.  Generally, a discrete random variable can be obtained by counting whereas a continuous random variable can be obtained by measuring.

Reflection

• What are the 4 characteristics of a binomial experiment?

1. The number of trials is constant.
2. Observations are independent.
3. There are two outcomes.
4. The probability of success is the same for each trial.

• Can we use a binomial distribution to model this process?

Yes, we can use a binomial distribution to model this process, since the process satisfies the four characteristics of the binomial experiment.

The trial estimate is fixed which in this case is 15 laptops. The observations made are independent, the results of one laptop do not affect the other. There are two outcomes which include failure or pass, the laptops either succeed to pass or fail to meet the requirements. The probability of success of all the laptops is 0.95, which is constant.

• What is the probability that the entire batch unnecessarily has to be tested if 95% of its laptops conform to specifications? (Hint: Use Excel's =BINOMDIST () function to find the probability)

The batch is considered acceptable provided no more than 1 laptop fails to meet specifications. Else, the entire batch must be tested in the second step. This means that if there are more than 1 laptops which are not meet the specifications then we need to test the entire batch.

Let X be the number of laptops that have not met the specifications.

Here X follows Binomial distribution with n = 15 and p = 1 - 0.95 = 0.05.

The obvious command to find the less than or equal to binomial probabilities in excel is "=BINOMDIST(x,n,p,1)"

Here x = 1, n = 15, p = 0.05

Therefore P(X ≤ 1) = "=BINOMDIST(1,15,0.05,1)" = 0.829047

Plugging this value in equation (1), we get

P(X > 1) = 1 - 0.829047 = 0.170953.

                                                      = 0.170953.

• What is the probability that the batch is incorrectly accepted if only 75% of its laptops conform to specifications?

Here probability of laptops conforms to specifications = 0.75

Therefore, the probability of laptops not conform to specifications = 1 - 0.75 = 0.25.

We accept the batch of laptops only when no more than 1 laptop does

 not conform to specifications.

 P(X ≤ 1).

Here n = 15, p = 0.25

So, P (X ≤ 1) = "=BINOMDIST (1,15,0.25,1)" = 0.080181.

                                                                                           = 0.080181

• What situations in your organization might this type of analysis apply to? Explain.

The Binomial distribution can be applied in my organization when computing the probability of events where only two possible outcomes can occur. For instance, when determining whether I made profits from a new product, the outcome is whether I made profits from the product (YES) or I did not make any profits (NO).

Another situation is an incidence of disease, for instance, flu which is highly transmittable. The probability that out of n workers in my organization, x workers will suffer from the flu (YES) or not (NO).