This question is incomplete, the complete answer is;
If one scours the Internet for long enough, one can collect the heights and weights of all of the players in the National Hockey League (... yes, we did!) If you did too, you would find that they have a mean height of 73.03 inches with a standard deviation of 2.03 inches. The mean weight would be 202.18 pounds with a standard deviation of 15.73 pounds. Here are some data for four of those NHL players in 2017-18: Player/Team HEIGHT WEIGHT Dustin Byfuglien (Winnipeg Jets) 75 260 Dylan Ferguson (Vegas Golden Knights) 74 190 Tom Wilson (Washington Capitals) 76 218 Sidney Crosby (Pittsburgh Penguins) 71 200.
Below, match each of the four players with their respective z-scores for height.
a. Dustin
b. Ferguson
c. Wilson
d. Crosby
1. A= 0.97
2. B= 0.48
3. C= -1.00
4. D= +1.46
Answer:
a. Dustin MATCHES 1. A= 0.97
b. Ferguson MATCHES 2. B= 0.48
c. Wilson MATCHES 4. D= +1.46
d. Crosby MATCHES 3. C= -1.00
Explanation:
Given that;
their mean height u = 73.03
standard deviation α = 2.03
now the z-score height for each player;
a- Dustin Byfuglien (Winnipeg Jets) Height = 75
z = (x - u) / α = (75 - 73.03) / 2.03 = 1.97 / 2.03 = 0.9704 ≈ 0.97
b- Dylan Ferguson (Vegas Golden Knights) Height = 74
z = (x - u) / α = (74 - 73.03) / 2.03 = 0.97 / 2.03 = 0.4778 ≈ 0.48
- Tom Wilson (Washington Capitals) Height = 76
z = (x - u) / α = (76 - 73.03) / 2.03 = 2.97 / 2.03 = 1.4630 ≈ 1.46
Sidney Crosby (Pittsburgh Penguins) Height = 71
z = (x - u) / α = (71 - 73.03) / 2.03 = -2.03 / 2.03 = - 1.00
Therefore
a. Dustin MATCHES 1. A= 0.97
b. Ferguson MATCHES 2. B= 0.48
c. Wilson MATCHES 4. D= +1.46
d. Crosby MATCHES 3. C= -1.00