Answer to Question #136874 in Statistics and Probability for Paras Gupta

Question

You are a first-year student studying at a leading Business School and would like to study the annual packages offered to the students under management domain. To conduct this study, you went to the placement team and asked for related data. Placement team has provided you the data as follows:

Highest package offered = INR 20,00,000

Lowest package offered = INR 5,00,000

Also, you were informed that first-year salaries of management graduates is normally distributed with the population mean μ= INR 9,00,000 and the population standard deviation σ = INR 2,00,000. Find the probability of a randomly selected management graduate from the business school earning less than INR 7,00,000 annually

Answer 1

Let $X=$ salaries of management graduates : $X\sim N(\mu, \sigma^2).$

Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1).$

Given $\mu=INR \ 900,000, \sigma=INR \ 200,000$

$$P(X<700000)=P(Z<\dfrac{700000-900000}{200000}=$$

$$=P(Z<-1)\approx0.158655$$