The State College Spikes evaluate potential players for center field based on tw

Question

The State College Spikes evaluate potential players for center field based on two main characteristics,
speed and strength.
a) Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating
more desirable (faster) speeds. From previous speed data for all players in this position, the times to
run 40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum
time of 4.40 seconds, as shown in the table below.
Mean Minimum
Time to run 40 yards (seconds) 4.6 0.15 4.4
Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable
to believe that the distribution of 40-yard running times is approximately normal? Explain.
b) Strength is measured by the amount of weight lifted, with more weight indicating more desirable
(greater) strength. From previous strength data for all players in this position, the amount of weight
lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below.
Mean
Amount of weight lifted (pounds) 310 25
Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.
c) The characteristics of speed and strength are considered to be of equal importance to the team in
selecting a player for the position. Based on the information about the means and standard deviations
of the speed and strength data for all players and the measurements listed in the table below for Players
A and B, which player should the team select if the team can only select one of the two players? Justify
your answer.
Time to run 40 yards (seconds) Player A PlayerB 4.42 4.57 Amount of weight lifted (pounds) 370 375

Explanation / Answer

Mean = 4.60 seconds

SD = 0.15 seconds

Minimum = 4.40 seconds

For judging normality there are many tools. With this minimum data, we can think on the basis of Sigma limits.

1 Limits are Mean-SDMean+SD

In this example it is 4.60-0.154.60+0.15

4.454.75

2 Limits are Mean-2*SDMean+2*SD

In this example it is 4.60-2*0.154.60+2*0.15

4.304.90

3 Limits are Mean-3*SDMean+3*SD

In this example it is 4.60-3*0.154.60+3*0.15

4.155.05

The minimum speed lies in lower part of 1 and 2

Mean Strength = 310 pounds and

SD of strength = 25 pounds.

Z score of a player who lift the weight of 370 pounds

= (X-Mean)/SD

= (370-310)/25

= 60/25

= 2.4

% CV

% CV

In the data for mean of two players for two characteristics is given. As values of SD are based on previous data, we can use them for calculating % CV.

From the calculations of % CV it is seen that, with regards to speed and Strength Player B is more consistent, hence one can give preference in selecting player B than A.

% CV

% CV

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