students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treating this class as the population, what percent of students study more than 12 hours a week

Use z-scores.

Formula:
z = (x - mean)/sd

Once you have the z-score, use the z-table to find the probability. Convert to a percentage.

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To calculate the percentage of students who study more than 12 hours a week, we first need to standardize the values using the population mean and standard deviation.

The formula for standardization (z-score) is given by:
z = (x - μ) / σ

where:
- z is the standardized value
- x is the individual value
- μ is the population mean
- σ is the population standard deviation

In this case, we have:
x = 12 hours (value we are interested in)
μ = 9.92 hours (population mean)
σ = 4.54 hours (population standard deviation)

Now, let's calculate the z-score:
z = (12 - 9.92) / 4.54
z = 2.08 / 4.54
z = 0.4586

Since we are interested in finding the percentage of students who study more than 12 hours a week, we need to find the area under the normal curve to the right of the z-score. We can use a standard normal distribution table or a calculator to find this value.

Using a standard normal distribution table or calculator, we find that the area to the right of z = 0.4586 is approximately 0.3228.

To convert this to a percentage, we multiply by 100:
0.3228 * 100 = 32.28%

Therefore, approximately 32.28% of students in this class study more than 12 hours a week.