Standard Deviation of basketball player height

In summary, the mean height of players in a basketball competition is 184 cm with a standard deviation of 5 cm. Using a normal distribution model, we can estimate the percentage of players likely to have certain heights. Approximately 68% are likely to be taller than 179 cm, 68% are likely to be taller than 189 cm, and 95% are likely to fall between 174 cm and 199 cm. It can also be estimated that only about 0.3% of players will be over 199 cm tall.
  • #1
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Homework Statement


The mean height of players in a basketball competition is 184 cm. If the standard deviation is 5 cm, what percentage of them are likely to be:
a) taller than 189 cm
b) taller than 179 cm
c) between 174 cm and 199 cm
d) over 199 cm cm tall?


Homework Equations


The textbook reads that often approximately 68 percent of the population will have a measure that fall sbetween 1 standard deviation either side of the mean, 95 percent 2 standard deviations either side of the mean, and 99.7 percent of the population 3 standard deviations either side of the mean.

The Attempt at a Solution


For the question above, how do I find the percentage? Using the information above, can I conclude that the percentile difference between s+1 and s-1 is 68 percent (where s= standard deviation, sorry I don't have the math application required by the website). Thank you.
 
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  • #2
I think you could model the given information to a normal distribution i.e. X~N(184,25) and then use some method (calculator, tables etc.) to calculate the probability of a certain height range occurring.
 
  • #3


Yes, you can use the information provided in the textbook to find the percentages for each scenario.

a) To find the percentage of players taller than 189 cm, you can use the 68-95-99.7 rule. Since 189 cm is one standard deviation above the mean (184 cm), we can estimate that about 68% of players will be taller than 189 cm.

b) Similarly, you can estimate that about 68% of players will be taller than 179 cm, as it is one standard deviation below the mean.

c) To find the percentage of players between 174 cm and 199 cm, we can use the 95% rule. Since 174 cm is two standard deviations below the mean and 199 cm is two standard deviations above the mean, we can estimate that about 95% of players will fall within this range.

d) Finally, to find the percentage of players over 199 cm tall, we can use the 99.7% rule. Since 199 cm is three standard deviations above the mean, we can estimate that about 99.7% of players will be taller than 199 cm.

Overall, the percentage may not be exact, but it can give you a good estimate based on the given information.
 

1. What is the Standard Deviation of basketball player height?

The Standard Deviation of basketball player height is a measure of how spread out the heights of basketball players are from the average height. It tells us how much the individual heights deviate from the mean height of all basketball players.

2. Why is the Standard Deviation important in basketball?

The Standard Deviation is important in basketball because it gives us an idea of the diversity of player heights in the sport. It can help coaches and scouts identify players who may have a height advantage or disadvantage, and it can also be used to compare the height distribution of different teams or leagues.

3. How is the Standard Deviation calculated for basketball player height?

The Standard Deviation is calculated by finding the average of the squared differences between each player's height and the mean height, and then taking the square root of that value. It can be calculated manually or with the help of statistical software.

4. What factors can affect the Standard Deviation of basketball player height?

The Standard Deviation of basketball player height can be affected by a variety of factors, including age, gender, genetics, and geography. For example, the Standard Deviation may be higher for younger players who are still growing, or for players from regions known for producing taller individuals.

5. Can the Standard Deviation of basketball player height change over time?

Yes, the Standard Deviation of basketball player height can change over time. This can happen due to factors such as changes in training methods and nutrition, or the influx of players from different regions or demographics. It is important to regularly analyze and update the Standard Deviation to accurately reflect the current height distribution of basketball players.

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