Question

A judgmental professor classifies students into three categories: • Worthy of a letter of recommendation: Such students are fully engaged in class, work well with others, follow instructions, attend office hours to clarify misconceptions, and try to understand topics. These students will earn internships and will be highly recruited. • Disruptive: These students either skip class or choose to be distracted in class (e.g. stare at cell phone when instructional staff is sharing and during team problems). Such students copy solutions and are not employable. • All other students. The professor has determined that 20% of students are worthy of a letter of recommendation and that 10% are disruptive. The amount of scholarship a student earns depends upon their classification. • Students worthy of a letter of recommendation receive an amount that is uniformly distributed between $1,000 and $2,000. • Disruptive student receive $0 with probability 1. • All other students receive a normally distributed amount with mean $500 and standard deviation $250. A student is selected at random. Determine the standard deviation of the scholarship amount the student receives.

Answer 1

20% Students worthy of a letter of recommendation receive an amount that is uniformly distributed between $1,000 and $2,000. • 10% Disruptive student receive $0 with probability 1. • All other students (70%) receive a normally distributed amount with mean $500 and standard deviation $250. .

The random variable representing the scholarship amount the student receives is

Assuming independence,

The standard deviation is