Finding Proportions and Scores
An investigator polls common cold sufferer, asking them to estimate the number of hours of physical discomfort caused by their most recent colds. Assume that their estimates approximate a normal curve with a mean of 83 hours and a standard deviation of 20 hours. (a) What is the estimated number of hours for the shortest-suffering 5 percent? (b) What proportion of sufferers estimate that their colds lasted longer than 48 hours? (c) What proportion suffered for fewer than 61 hours? (d) What is the estimated number of hours suffered by the extreme 1 percent either above or below the mean? (e) What proportion suffered for between 1 and 3 days, that is, between 24 and 72 hours? (f) What is the estimated number of hours suffered by the middle 95 percent? [See the comment about “middle 95 percent” in Question 5.13(d).] (g) What proportion suffered for between 2 and 4 days? (h) A medical researcher wishes to concentrate on the 20 percent who suffered the most. She will work only with those who estimate that they suffered for more than ——— hours. (I) Another researcher wishes to compare those who suffered least with those who suffered most. If each group is to consist of only the extreme 3 percent, the mild group will consist of those who suffered for fewer than _____ hours, and the severe group will consist of those who suffered for more than _____ hours. (j) Another survey found that people with colds who took daily doses of vitamin C suf-fered, on the average, for 61 hours. What proportion of the original survey (with a mean of 83 hours and a standard deviation of 20 hours) suffered for more than 61 hours? (k) What proportion of the original survey suffered for exactly 61 hours?