Question

• the mean height of the players on team a is 5 feet 8 inches.
• the mean height of the players on team b is 5 feet 10 inches.
• the height of the shortest player on each of the teams is 5 feet 5 inches.

two new players, tara and laney, sign up to join the teams. tara is 5 feet 9 inches tall and laney is shorter than tara.
the coach decides to put them on the same team. the heights of the new players are measured, and the mean team heights are recalculated.
select the statement that will always be correct.
a if the coach puts tara and laney on team a, the mean height of the players on team a will be taller than 5 feet 8 inches.
b if the coach puts tara and laney on team a, the mean height of the players on team a will be shorter than 5 feet 8 inches.
c if the coach puts tara and laney on team b, the mean height of the players on team b will be taller than 5 feet 10 inches.
d if the coach puts tara and laney on team b, the mean height of the players on team b will be shorter than 5 feet 10 inches.

Explanation:

Step1: Analyze Option A

Team A's original mean is 5 feet 8 inches. Tara is 5 feet 9 inches (taller than the mean) and Laney is shorter than Tara. But even if Laney is very short (minimum 5 feet 5 inches), since Tara is taller than the mean, the new mean will be taller than 5 feet 8 inches.

Step2: Analyze Option B

As shown in Step1, Option B is incorrect.

Step3: Analyze Option C

Team B's original mean is 5 feet 10 inches. Tara is 5 feet 9 inches (shorter than the mean) and Laney is shorter than Tara. So the new mean will be shorter than 5 feet 10 inches, not taller.

Step4: Analyze Option D

Team B's original mean is 5 feet 10 inches. Tara is 5 feet 9 inches (shorter than the mean) and Laney is shorter than Tara. So the new mean will be shorter than 5 feet 10 inches. But we need to check if it's always true. Suppose there are a large number of players on Team B. Adding two shorter - than - mean players will pull the mean down.

Answer:

A. If the coach puts Tara and Laney on Team A, the mean height of the players on Team A will be taller than 5 feet 8 inches.