In a random sample of 150 community college students, the mean number of hours spent studying per week is 11.7 hours and the standard deviation is 4 hours.
a) Find the standard score (z-score) for students who study the following hours in a particular week. Round Z to the nearest hundredth and interpret the meaning of each answer as it pertains to this problem.
b) Assuming the distribution of the number of hours community college students study per week is normally distributed, approximately how many of the students in the sample study between 7.7 and 15.7 hours per week?
c) Assuming the distribution of the number of hours community college students study per week is normally distributed, approximately how many of the students in the sample study less than 3.7 hours per week?
d) Without assuming anything about the distribution of the number of hours community college students study per week, at least what percentage (approximately) of the students study between 5.3 and 18.1 hours per week?
e) Without assuming anything about the distribution of the number of hours community college students study per week, at most what percentage of the students study less than 3.7 hours or more than 19.7 hours per week?