Claire and George are tasked with decorating Easter eggs.

Question

The amount of eggs that Claire can decorate in an hour is a random variable with 𝜇� = 16 and 𝜎� = 4. The amount of eggs that George can decorate in an hour is a random variable with 𝜇� = 17 and 𝜎� = 4. Assume the amount of eggs Claire and George decorate are independent of each other. (Round your answers to four decimal places, if needed.)

(a) What is the mean for the total number of eggs they decorate in an hour?

Answer: 

Your last answer was interpreted as follows:

3333

(b) What is the standard deviation for the total number of eggs they decorate in an hour?

Answer: 

(c) Claire decides to decorate Easter eggs for one hour today and for another hour tomorrow. What is the expected value of the total number of eggs she will decorate in total?

Answer: 

(d) Claire decides to decorate Easter eggs for one hour today and for another hour tomorrow. What is the standard deviation of the total number of eggs she will decorate in total?

Answer: 

Answer 1

Claire: μ₁ = 16 and σ₁ = 4

George: μ₂ = 17 and σ₂ = 4

a.) The mean for the total number of eggs they decorate in an hour is the sum of their individual means.

μ_total = μ₁ + μ₂ = 16 + 17 = 33

b.) The standard deviation for the total number of eggs they decorate in an hour is the square root of the sum of their individual variances since they are independent.

σ_total = √(σ₁)² + (σ₂)² = √4² + 4² = √16 + 16 = √32 ≈ 5.6569

c.) The expected value of the total number of eggs Claire will decorate in total is the sum of the expected values for each hour.

E = μ1*(number of hours) = 16 * 2 = 32

d.) The standard deviation of the total number of eggs Claire will decorate in total is the square root of the sum of the variances for each hour since they are independent.

σ_total = √(σ₁)²×(number of hours) = √4² × 2 = √16*2 = √32 ≈ 5.6569