What percentages of students studied 30 hours or less? These hours ranged between 10-50 hours with a mean of 35 and a standard deviation of 5.
To find the percentage of students who studied 30 hours or less, we need to use z-scores and the standard normal distribution.
First, let's calculate the z-score of 30 using the formula:
z = (x - μ) / σ
where x is the value we are interested in (30), μ is the mean (35), and σ is the standard deviation (5).
Substituting the values into the formula:
z = (30 - 35) / 5
z = -1
Next, we need to find the cumulative probability associated with this z-score. This represents the area under the standard normal distribution curve to the left of the z-score.
Using a standard normal distribution table or a statistical calculator, we find that the cumulative probability associated with a z-score of -1 is approximately 0.1587.
To convert this cumulative probability to a percentage, we multiply by 100:
percentage = 0.1587 * 100
percentage ≈ 15.87%
So, approximately 15.87% of students studied 30 hours or less.