Refer to Example 4.6. The probability distribution for the time to evacuate in the event of a hurricane, Table 4.4, is reproduced here. Weather forecasters say they cannot accurately predict a hurricane landfall more than 14 hours in advance. If the Gulf Coast Civil Engineering Department waits until the 14-hour warning before beginning evacuation, what is the probability that all residents of low-lying areas are evacuated safely (i.e., before the hurricane hits the Gulf Coast)?

Table 4.4

Data from Example 4.6

A panel of meteorological and civil engineers studying emergency evacuation plans for Florida’s Gulf Coast in the event of a hurricane has estimated that it would take between 13 and 18 hours to evacuate people living in low-lying land with the probabilities shown in Table 4.4.
a. Calculate the mean and standard deviation of the probability distribution of the evacuation times.
b. Within what range would you expect the time to evacuate to fall?

Time to Evacuate (nearest hour) Probability 13 .04 14 .25 15 .40 16 .18 17 .10 18 .03