Standard Deviation of basketball player height

[L²Cc]

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.

 

[danago]

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.

 

[Architeuthis Dux]

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.