Answer to Question #308509 in Statistics and Probability for Aarti

Question

Q.You have been hired as a researcher for a prominent research-based organization and you have been allocated a new project for helping out a client.

You know that the time taken to complete similar projects is normally distributed with a mean of 50 days and a standard deviation of 4 days.  

 

a. What is the probability of finishing this project within 45 – 55 days? (5 Marks) 

b. When do we use Poisson Distribution? Give two example scenarios. (5 Marks)

Answer 1

a. We have a normal distribution, $\mu=50, \sigma=4.$

Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma};$

$z_1=\cfrac{45-50}{4}=-1.25, z_2=\cfrac{55-50}{4}=1.25,$

$P(45<X<55)=P(-1.25<Z<1.25)=P(Z<1.25)-P(Z<-1.25)=$

$=0.89435-0.10565=0.7887$ (from z-table).

b. The Poisson distribution describes the probability of a certain number of events occurring during some time period. For the most part, you may use past data to determine this probability and learn about the frequency of events.

There are many sectors where Poisson distribution can be used for predicting the probabilities of an event. It is used in many scientific fields and is also popular in the business sector. A few of the examples are stated below.

1. Checking for the amount of a product needed throughout a year. If a business/ supermarket/ store knows the average amount of the products used in a year by their customers, they can use the Poisson distribution model to predict in which month the product sells more. This can help them store the required amount of the product and prevent their losses.

2. It can be used to predict the probability of an occurrence of floods, storms, and other natural disasters. This can be possible if the average number of such disasters per year is known. With these predictions, along with other technological applications, it is possible to avoid human and property losses for many countries or regions.