Question
Decide whether the following statement makes sense or does not make
sense.
The heights of male basketball players at a local college are normally
distributed with a mean of 6 feet 3 inches and a standard deviation of 3
inches.
Choose the correct answer below.
Makes sense
Does not make sense
sense.
The heights of male basketball players at a local college are normally
distributed with a mean of 6 feet 3 inches and a standard deviation of 3
inches.
Choose the correct answer below.
Makes sense
Does not make sense
Ask by Hammond Dunn. in the United States
Jan 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The statement makes sense.
Solution
To determine whether the statement makes sense, we need to consider the characteristics of a normal distribution, particularly in the context of human heights.
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Mean Height: The mean height of male basketball players is stated to be 6 feet 3 inches, which is approximately 75 inches. This is a reasonable average height for male basketball players, as they tend to be taller than the general population.
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Standard Deviation: The standard deviation is given as 3 inches. In a normal distribution, the standard deviation indicates how much variation or dispersion there is from the mean. A standard deviation of 3 inches is relatively small compared to the mean height of 75 inches, suggesting that most players’ heights would fall within a narrow range around the mean.
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Distribution Characteristics: In a normal distribution, about 68% of the data falls within one standard deviation of the mean. For this case, that would mean approximately 68% of the players would have heights between 72 inches (6 feet) and 78 inches (6 feet 6 inches). This range is plausible for male basketball players.
Given these points, the statement about the heights of male basketball players being normally distributed with a mean of 6 feet 3 inches and a standard deviation of 3 inches makes sense.
Final Answer: Makes sense.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
Does not make sense. While the statement presents a mean height of 6 feet 3 inches, a standard deviation of 3 inches is unusually large for a normally distributed set of male heights. Typically, you’d expect the heights of college basketball players to have a standard deviation closer to 1-2 inches. A 3-inch variation might suggest that the distribution is more spread out than one would typically observe in this population.
To put this into perspective, for most athletic populations, especially in basketball where players are generally taller, a standard deviation exceeding 2 inches could imply significant extremes in height, leading to a skewed representation of what you would expect across a team or college roster.
