Asked by Elia Adele Marcheline on Jun 09, 2024
Verified
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.What percent of players weigh between 175 and 225 pounds?
A) 50%
B) 68.27%
C) 31.73%
D) 95%
Standard Deviation
A measure of the amount of variation or dispersion in a set of values, indicating how much individual values differ from the mean.
Football Players
Athletes who participate in football, a team sport involving the passing and kicking of a ball to score points.
- Acquire insight into the particularities and applicative contexts of the normal distribution.
- Derive probabilities and percentages linked to normal distributions.
- Decode the relationship existing among standard deviation, mean, and distribution effects.
Verified Answer
MD
Megan DeGuzmanJun 13, 2024
Final Answer :
B
Explanation :
We can solve this problem using the empirical rule or z-score table.
Empirical rule:
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
Since 175 and 225 are each 1 standard deviation away from the mean of 200, we know that about 68% of the data falls between these two values.
Therefore, the best choice is B) 68.27%.
Empirical rule:
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
Since 175 and 225 are each 1 standard deviation away from the mean of 200, we know that about 68% of the data falls between these two values.
Therefore, the best choice is B) 68.27%.
Learning Objectives
- Acquire insight into the particularities and applicative contexts of the normal distribution.
- Derive probabilities and percentages linked to normal distributions.
- Decode the relationship existing among standard deviation, mean, and distribution effects.