Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
Step-by-step explanation:
To determine the least amount of protein that places high school athletes in the middle 7.63% of the distribution, we need to find the protein intake values corresponding to the lower and upper bounds of the middle 7.63%. This can be done by determining the z-scores corresponding to the percentiles for the middle 7.63%.
Here are the steps:
Determine the z-scores for the middle 7.63% of a normal distribution:
The middle 7.63% implies that we are excluding 100% - 7.63% = 92.37% from the distribution.
This 92.37% is split equally on both sides of the middle. So, we have 46.185% in each tail.
Calculate the z-scores for these percentiles:
The lower percentile (left tail) is 46.185%.
The upper percentile (right tail) is 53.815% (since 50% + 3.815%).
To find these z-scores, we use the inverse of the cumulative distribution function (CDF) for a standard normal distribution.
Convert z-scores to protein intake values:
Use the z-score formula: x=μ+z⋅σx=μ+z⋅σ
Where μμ is the mean protein intake (116.94 grams).
σσ is the standard deviation (26.31 grams).
Let's perform these calculations:
Find the z-scores for the percentiles.
Convert these z-scores to actual protein intake values.
First, let's find the z-scores.
For 46.185%46.185%:
z1=norm.ppf(0.46185)z1=norm.ppf(0.46185)
For 53.815%53.815%:
z2=norm.ppf(0.53815)z2=norm.ppf(0.53815)
Now, convert these z-scores to protein intake values:
x1=μ+z1⋅σx1=μ+z1⋅σ
x2=μ+z2⋅σx2=μ+z2⋅σ
Since we need the least amount of protein, we focus on the lower bound:
x1=116.94+z1⋅26.31x1=116.94+z1⋅26.31
Let's calculate this.
The least amount of protein that places high school athletes in the middle 7.63% of the distribution is approximately 114.4202 grams. This is the minimum protein intake that ensures they are getting enough for their developing bodies.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
