In the 4 × 100 relay event,each of four runners runs 100 metres.A university team is preparing for a competition.The means and standard deviations of the times (in seconds)of their four runners are as shown in the table:
What are the mean and standard deviation of the relay team's total time in this event? Assume that the runners' performances are independent.
A)μ = 48.3 sec,σ = 12.64 sec
B)μ = 48.3 sec,σ = 0.045 sec
C)μ = 24.15 sec,σ = 0.21 sec
D)μ = 48.3 sec,σ = 0.21 sec
E)μ = 24.15 sec,σ = 12.64 sec

Question

In the 4 × 100 relay event,each of four runners runs 100 metres.A university team is preparing for a competition.The means and standard deviations of the times (in seconds)of their four runners are as shown in the table: 
What are the mean and standard deviation of the relay team's total time in this event? Assume that the runners' performances are independent.
A)μ = 48.3 sec,σ = 12.64 sec 
B)μ = 48.3 sec,σ = 0.045 sec 
C)μ = 24.15 sec,σ = 0.21 sec 
D)μ = 48.3 sec,σ = 0.21 sec 
E)μ = 24.15 sec,σ = 12.64 sec

Quizplus · Accepted Answer

The mean of the total time for the team can be found by adding up the means of the individual runners. 
μ = 12.3 sec + 12.1 sec + 12.8 sec + 11.1 sec = 48.3 sec

The variance of the total time for the team can be found by adding up the variances of the individual runners. Since the runners' performances are independent, the variance of the sum is the sum of the variances.
σ^2 = 1.6^2 + 1.2^2 + 2.5^2 + 0.6^2 = 12.64
So, the standard deviation of the total time is the square root of the variance:
σ = √12.64 = 3.56 sec ≈ 0.21 sec

Therefore, the best choice is D.

In the 4 × 100 Relay Event,each of Four Runners