The new player's personal time is 4.5 seconds.
<h3>What is the new player's personal time?</h3>
The first step is to determine the total time the 5 persons complete the dash.
Total time = 5 x 5.7 = 28.5 seconds
The second step is to determine the total time for the 6 people to complete the dash.
Total time = 6 x 5.5 = 33 seconds
The third step is to find the difference of the time in the previous two steps: 33 - 28.5 = 4.5 seconds
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The answer is 5.5
The standard deviation (sd or σ) of the sample mean difference is:
sd = √(sd₁²/n₁ + sd₂²/n₂)
For the population A:
sd₁ = 17.6
n₁ = 25
For the population B:
sd₂ = 21.2
n₂ = 30
Hence:
sd = √(sd₁²/n₁ + sd₂²/n₂)
= √(17.6²/20 + 21.2²/30)
= √(309.76/20 + 449.44/30)
= √(15.49 + 14.98)
= √(30.47)
= 5.5