Thomas Myers is a staff physician at the clinic in Grand Canyon Village. Based on reports in recent years, Dr. Myers estimates that about 31% of the boating accidents on the Colorado River in Grand Canyon National Park occur at Crystal Rapids (mile 98). These range from small accidents (a few bruises) to major accidents (death).
(a) What is the probability that at least 25% of these accidents occurred at Crystal Rapids?
(b) What is the probability that between 25% and 50% (including 25% and 50%) of these accidents occurred at Crystal Rapids?
(c) Is the normal approximation to the proportion p̂ = r/n valid in this application? Explain.