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 determine the percentage of students who studied 30 hours or less, we need to calculate the z-score for 30 hours and then use a standard normal distribution table (also known as a z-table).
The formula for calculating the z-score is: z = (x - μ) / σ
Where:
- x is the value we want to calculate the z-score for (in this case, 30 hours)
- μ is the mean (35 hours)
- σ is the standard deviation (5 hours)
Let's calculate the z-score for 30 hours:
z = (30 - 35) / 5
z = -1
Using a standard normal distribution table (z-table), we can find the percentage of students who studied 30 hours or less. Look up the z-score of -1 in the z-table. The closest value we can find is z = -1.00. The corresponding percentage in the table is 34.13%.
Therefore, approximately 34.13% of students studied 30 hours or less.