Final answer:
Without knowing the standard deviation, it is impossible to conclusively determine the true or false nature of the statement regarding the percentage of students who study over 8 hours. The t-distribution is used to test study habits with unknown population standard deviations, but the normal distribution is used when the population standard deviation is known.
Step-by-step explanation:
The statement about the distribution of study hours for students is incomplete because it does not provide the standard deviation required to determine whether the statement '1 percent of students study over 8 hours' is true or false. To determine this, one would need to know the exact standard deviation and apply the z-score formula to calculate the percentage of students who study more than a certain number of hours per week. However, if we do know that the mean is 6.5 hours, then in a normal distribution, it's likely that 1 percent of students would be more than a certain number of standard deviations away from the mean, which could be at or beyond 8 hours of study depending on that standard deviation.
The distribution that would be used to test study habits or study time is typically the t-distribution when working with sample means and unknown population standard deviations. This distribution is appropriate when the sample size is small and the population standard deviation is unknown. However, if the population standard deviation is known, as in some provided cases, the normal distribution or Z-distribution would be used instead.