Answer to Question #209185 in Statistics and Probability for Novella

Question

A global financial institution transfers a large data file every evening from offices around the world to its London headquarters. Once the file is recieved, it must be cleaned and partitioned before being stored in a company's data warehouse. Each file is the same size and the time required to transfer, clean, and partition a file is normally distributed, with a mean of 1.5 hours and standard deviation of 15 minutes. If a manager must be present until 85% of the files are transferred, cleaned, and partitioned, how long will the manager need to be there?

Answer 1

Let $X=$ the time required to transfer: $X\sim N(\mu, \sigma^2).$

Given $\mu=90, \sigma=15.$

$$P(X<x)=P(Z<\dfrac{x-90}{15})=0.85$$

$$\dfrac{x-90}{15}\approx1.036433$$

$$x=105.5\ min$$