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)
About 80%
About 95%
About 40%
About 84%

Answer 1

The percentage of college students who sleep between 5 and 10 hours is approximately 84%, calculated using z-scores and the standard normal distribution.

Step-by-step explanation:

The question asks us to calculate the percentage of college students who sleep between 5 and 10 hours on a week night, given that sleep time is normally distributed with a mean of 7 hours and a standard deviation of 1.7 hours. To do this, we use a z-table and the standard normal distribution.

First, we calculate the z-scores for 5 and 10 hours:

• Z-score for 5 hours = (5 - 7) / 1.7 ≈ -1.18
• Z-score for 10 hours = (10 - 7) / 1.7 ≈ 1.76

Using the z-table, we find the corresponding probabilities:

• Probability for Z ≤ -1.18 ≈ 0.1190
• Probability for Z ≤ 1.76 ≈ 0.9608

To find the probability of being between these z-scores, we subtract the smaller probability from the larger one:

0.9608 - 0.1190 ≈ 0.8418

The percentage of students who sleep between 5 and 10 hours is approximately 84%. Thus, the correct answer is About 84%.