Question

A consultant has three sources of income—from teaching short courses, from selling computer software, and from advising on projects. His expected annual incomes from these sources are $7,000, $22,000, and $50,000, and the respective standard deviations are $3,000, $4,000, and $18,000. Assuming independence, find the mean and standard deviation of his total annual income.

Answer 1

Mean = $79,000

Standard deviation = $25,000

Explanation:

Data provided in the question:

Expected annual incomes:

From teaching short courses = $7,000

From selling computer software = $22,000

From advising on projects = $50,000

Standard deviation:

teaching short courses = $3,000

selling computer software = $4,000

advising on projects = $18,000

Now,

it is given that the events are independent

therefore,

Mean = ∑(Expected annual income)

or

Mean = $7,000 + $22,000 + $50,000

or

Mean = $79,000

also,

Standard deviation = ∑(standard deviation)

or

Standard deviation = $3,000 + $4,000 + $18,000 = $25,000