Question

The number of hours that college students sleep on a week night is approximated by a normal curve with a mean of 7 hours and a standard deviation of 1.7 hours. Answer the question below using a z table:

On a week night, what percentage of students sleep between 5 and 10 hours? (round to whole number)

Answer 1

To determine the answer to this item, we first calculate the z-scores of the given data point through the equation,

z-score = (data point - mean) / standard deviation
For 5:
z-score = (5 - 7) / 1.7 = -1.176
This translates to a percentile of 11.97.
For 10:
z-score = (10 - 7) / 1.7 = 1.76
This translates to a percentile of 96.08.
The difference between the percentiles is 84.11. Thus, 84% of the students sleep between 5 to 10 hours.