Participants from the National Health and Nutrition Examination Survey, 2003–2004, had a mean BMI of 28.3 with a standard deviation of 6.0. Assuming BMI is normally distributed, what proportion of the participants had a BMI measure over 35?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
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To find the proportion of participants with a BMI measure over 35, we can use the standard normal distribution and the z-score formula.
1. Calculate the z-score for the BMI value of 35 using the formula:
z = (x - μ) / σ
where x is the BMI value (35), μ is the mean BMI (28.3), and σ is the standard deviation (6.0).
z = (35 - 28.3) / 6.0
2. Calculate the z-score using the formula:
z = 6.7 / 6.0
Simplifying:
z = 1.12
3. Use a standard normal distribution table or a calculator to find the proportion of values to the right of the z-score of 1.12. This represents the proportion of participants with a BMI measure over 35.
From the standard normal distribution table or a calculator, the proportion to the right of z = 1.12 is approximately 0.1314.
Hence, approximately 13.14% (or 0.1314 proportion) of the participants had a BMI measure over 35.
To find the proportion of participants with a BMI measure over 35, we need to calculate the z-score and then use a standard normal distribution table or a statistical calculator.
First, let's calculate the z-score using the formula:
z = (x - μ) / σ
where x is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation.
In this case, we have:
x = 35
μ = 28.3
σ = 6.0
Plugging the values into the formula, we get:
z = (35 - 28.3) / 6.0
Now, we can use the z-score to find the proportion using a standard normal distribution table or a statistical calculator. The z-score represents the number of standard deviations the value is away from the mean.
Using a standard normal distribution table, we can find the proportion associated with the corresponding z-score. Look up the z-score in the table and find the proportion in the corresponding row and column.
Alternatively, you can use a statistical calculator or software to find the proportion directly. Most statistical calculators or software have built-in functions to calculate probabilities from a normal distribution.
After finding the proportion, remember that the standard normal distribution table provides the proportion to the left of the z-score. So, to find the proportion of participants with a BMI measure over 35, subtract the proportion you find from 1.
Note: The assumptions made in this calculation are that the data is normally distributed and the sample is representative of the population.