Question

Question on standard deviation/variance?

Kitchens - SD = 45 sq ft
Bedrooms - SD = 65 sq ft

The total area of a 3-bedroom house has a SD of 225 sq ft. What is the standard deviation of the area for living after the bedrooms and kitchen are excluded?

(the answer is 189 sq ft)

Answer 1

Variance can be summed as long as random variables are independent. Thus, variance of house = `225^2=50625`

Variance excluding bedrooms and kitchen = `50625 - 45^2 - 3*65^2 =35925`

Standard deviation = `sqrt{35925} \approx 189` sqft