In a recent study on american sleep habits 1500 adults were asked questions about their sleep cycles. the study found that 41 % say they get sleepy on the job and their work suffers at least a few days each month. an additional 22 % said the problems occur a few days each week and 7 % say sleepiness on the job is a daily occurrence. for the remaining respondents, sleepiness was not a problem at all.
summarize the given information by constructing a frequency and relative frequency distribution.

The weight of an object in a particular scale is 175.2 lbs. the measured weight may vary from the actual weight by at most 0.1 lbs. what is the range of actual weights of the object

Abox holds 500 paperclips. after a week on the teacher's desk 239 paperclips remained. how many paperclips were used?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.